From b11634787bb3bfe5746b9c12b17483fd41e65e9c Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:14:49 +0530
Subject: [PATCH 01/19] Overwrote methods concerning loops

---
 src/sage/graphs/matching_covered_graph.py | 25 ++++++++++++++++++-----
 1 file changed, 20 insertions(+), 5 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 2a9b8916c90..1221ee5f192 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -57,7 +57,6 @@
         ``delete_multiedge()`` | Delete all edges from ``u`` to ``v``.
         ``disjoint_union()`` | Return the disjoint union of ``self`` and ``other``.
         ``disjunctive_product()`` | Return the disjunctive product of ``self`` and ``other``.
-        ``has_loops()`` | Return whether there are loops in the matching covered graph.
         ``is_biconnected()`` | Check if the matching covered graph is biconnected.
         ``is_block_graph()`` | Check whether the matching covered graph is a block graph.
         ``is_cograph()`` | Check whether the matching covered graph is cograph.
@@ -69,12 +68,8 @@
         ``join()`` | Return the join of ``self`` and ``other``.
         ``lexicographic_product()`` | Return the lexicographic product of ``self`` and ``other``.
         ``load_afile()`` | Load the matching covered graph specified in the given file into the current object.
-        ``loop_edges()`` | Return a list of all loops in the matching covered graph.
-        ``loop_vertices()`` | Return a list of vertices with loops.
         ``merge_vertices()`` | Merge vertices.
-        ``number_of_loops()`` | Return the number of edges that are loops.
         ``random_subgraph()`` | Return a random matching covered subgraph containing each vertex with probability ``p``.
-        ``remove_loops()`` | Remove loops on vertices in ``vertices``.
         ``save_afile()`` | Save the graph to file in alist format.
         ``strong_product()`` | Return the strong product of ``self`` and ``other``.
         ``subdivide_edge()`` | Subdivide an edge `k` times.
@@ -1918,6 +1913,10 @@ def get_matching(self):
         """
         return self._matching
 
+    @doc_index('Overwritten methods')
+    def has_loops(self):
+        raise NotImplementedError()
+
     @doc_index('Overwritten methods')
     def has_perfect_matching(G, algorithm='Edmonds', solver=None, verbose=0,
                              *, integrality_tolerance=1e-3):
@@ -2003,6 +2002,22 @@ def has_perfect_matching(G, algorithm='Edmonds', solver=None, verbose=0,
         raise ValueError('algorithm must be set to \'Edmonds\', '
                          '\'LP_matching\' or \'LP\'')
 
+    @doc_index('Overwritten methods')
+    def loop_edges(self, labels=True):
+        raise NotImplementedError()
+
+    @doc_index('Overwritten methods')
+    def loop_vertices(self):
+        raise NotImplementedError()
+
+    @doc_index('Overwritten methods')
+    def number_of_loops(self):
+        raise NotImplementedError()
+
+    @doc_index('Overwritten methods')
+    def remove_loops(self, vertices=None):
+        raise NotImplementedError()
+
     @doc_index('Miscellaneous methods')
     def update_matching(self, matching):
         r"""

From f6ad99cbc2a7eb53d5e3f145c5e499c9fd65402e Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:18:28 +0530
Subject: [PATCH 02/19] Overwrote has_loops()

---
 src/sage/graphs/matching_covered_graph.py | 82 ++++++++++++++++++++++-
 1 file changed, 81 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 1221ee5f192..4426fd5b211 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1915,7 +1915,87 @@ def get_matching(self):
 
     @doc_index('Overwritten methods')
     def has_loops(self):
-        raise NotImplementedError()
+        r"""
+        Check whether thare are loops in the (matching covered) graph.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.generic_graph.GenericGraph.has_loops` method in
+            order to return ``False`` as matching covered graphs are always
+            free of looped edges.
+
+        OUTPUT:
+
+        - A boolean ``False`` is returned since matching covered graphs, by
+          definition, are free of self-loops.
+
+        EXAMPLES:
+
+        A matching covered graph, for instance the Petersen graph, is always free
+        of loops::
+
+            sage: P = graphs.PetersenGraph()
+            sage: G = MatchingCoveredGraph(P)
+            sage: G
+            Matching covered petersen graph: graph on 10 vertices
+            sage: G.has_loops()
+            False
+            sage: G.allows_loops()
+            False
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        A matching covered graph may support multiple edges, still no
+        loops are allowed::
+
+            sage: K = graphs.CompleteGraph(2)
+            sage: G = MatchingCoveredGraph(K)
+            sage: G.allow_multiple_edges(True)
+            sage: G
+            Matching covered complete graph: multi-graph on 2 vertices
+            sage: G.add_edge(0, 1, 'label')
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label')]
+            sage: G.allows_loops()
+            False
+            sage: G.has_loops()
+            False
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
+
+        """
+        return False
 
     @doc_index('Overwritten methods')
     def has_perfect_matching(G, algorithm='Edmonds', solver=None, verbose=0,

From 7de0b7be9bd2ff347e0eb0362ed50765bf8d5281 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:21:35 +0530
Subject: [PATCH 03/19] Overwrote loop_edges()

---
 src/sage/graphs/matching_covered_graph.py | 94 ++++++++++++++++++++++-
 1 file changed, 93 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 4426fd5b211..e6630415f34 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2084,7 +2084,99 @@ def has_perfect_matching(G, algorithm='Edmonds', solver=None, verbose=0,
 
     @doc_index('Overwritten methods')
     def loop_edges(self, labels=True):
-        raise NotImplementedError()
+        r"""
+        Return a list of all loops in the (matching covered) graph.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.generic_graph.GenericGraph.loop_edges` method
+            in order to return an empty list as matching covered graphs are
+            free of looped edges.
+
+        INPUT:
+
+        - ``labels`` -- boolean (default: ``True``); whether returned edges have
+         labels (``(u,v,l)``) or not (``(u,v)``)
+
+        OUTPUT:
+
+        - A list capturing the edges that are loops in the matching covered
+          graph; note that, the list is empty since matching covered graphs do
+          not contain any looped edges.
+
+        EXAMPLES:
+
+        A matching covered graph, for instance the Heawood graph, by
+        definition, is always free of loops::
+
+            sage: H = graphs.HeawoodGraph()
+            sage: G = MatchingCoveredGraph(H)
+            sage: G
+            Matching covered heawood graph: graph on 14 vertices
+            sage: G.has_loops()
+            False
+            sage: G.allows_loops()
+            False
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        A matching covered graph may support multiple edges, still no
+        loops are allowed::
+
+            sage: C = graphs.CycleGraph(4)
+            sage: G = MatchingCoveredGraph(C)
+            sage: G.allow_multiple_edges(True)
+            sage: G
+            Matching covered cycle graph: multi-graph on 4 vertices
+            sage: G.add_edge(0, 1, 'label')
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label'), (0, 3, None), (1, 2, None), (2, 3, None)]
+            sage: G.allows_loops()
+            False
+            sage: G.has_loops()
+            False
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        One may set the ``label`` to either ``True`` or ``False``::
+
+            sage: G.loop_edges(labels=False)
+            []
+            sage: G.loops(labels=True)
+            []
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
+        """
+        return []
 
     @doc_index('Overwritten methods')
     def loop_vertices(self):

From a5a332fb85330f0587f1426e3b8b4fdc83ca0fc9 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:24:06 +0530
Subject: [PATCH 04/19] Overwrote loop_vertices()

---
 src/sage/graphs/matching_covered_graph.py | 86 ++++++++++++++++++++++-
 1 file changed, 85 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index e6630415f34..e73d96367da 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2180,7 +2180,91 @@ def loop_edges(self, labels=True):
 
     @doc_index('Overwritten methods')
     def loop_vertices(self):
-        raise NotImplementedError()
+        """
+        Return a list of vertices with loops.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.generic_graph.GenericGraph.loop_vertices`
+            method in order to return an empty list as matching covered graphs
+            are free of vertices that have looped edges.
+
+        OUTPUT:
+
+        - A list capturing the vertices that have loops in the matching covered
+          graph; note that, the list is empty since matching covered graphs do
+          not contain any looped edges.
+
+        EXAMPLES:
+
+        A matching covered graph, for instance the Möbius graph of order 8, by
+        definition, is always free of loops::
+
+            sage: M = graphs.MoebiusLadderGraph(4)
+            sage: G = MatchingCoveredGraph(M)
+            sage: G
+            Matching covered moebius ladder graph: graph on 8 vertices
+            sage: G.has_loops()
+            False
+            sage: G.allows_loops()
+            False
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        A matching covered graph may support multiple edges, still no
+        loops are allowed::
+
+            sage: S = graphs.StaircaseGraph(4)
+            sage: G = MatchingCoveredGraph(S)
+            sage: G.allow_multiple_edges(True)
+            sage: G
+            Matching covered staircase graph: multi-graph on 8 vertices
+            sage: G.add_edge(0, 1, 'label')
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label'), (0, 3, None), (0, 6, None),
+             (1, 2, None), (1, 4, None), (2, 5, None), (2, 7, None),
+             (3, 4, None), (3, 6, None), (4, 5, None), (5, 7, None),
+             (6, 7, None)]
+            sage: G.allows_loops()
+            False
+            sage: G.has_loops()
+            False
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
+
+        """
+        return []
 
     @doc_index('Overwritten methods')
     def number_of_loops(self):

From 8979db1d7c2abbb48ec0dfd82a9e47265a8b5ce2 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:26:57 +0530
Subject: [PATCH 05/19] Overwrote loops()

---
 src/sage/graphs/matching_covered_graph.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index e73d96367da..133d86e32ac 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2266,6 +2266,8 @@ def loop_vertices(self):
         """
         return []
 
+    loops = loop_edges
+
     @doc_index('Overwritten methods')
     def number_of_loops(self):
         raise NotImplementedError()

From 7acc34d42283ea1c4a906105d0ffcf4e23a8d7eb Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:27:55 +0530
Subject: [PATCH 06/19] Overwrote number_of_loops()

---
 src/sage/graphs/matching_covered_graph.py | 84 ++++++++++++++++++++++-
 1 file changed, 83 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 133d86e32ac..77b3654374c 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2270,7 +2270,89 @@ def loop_vertices(self):
 
     @doc_index('Overwritten methods')
     def number_of_loops(self):
-        raise NotImplementedError()
+        r"""
+        Return the number of edges that are loops.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.generic_graph.GenericGraph.number_of_loops`
+            method in order to return 0 as matching covered graphs are free
+            of looped edges.
+
+        OUTPUT:
+
+        - An integer, 0 is returned, since matching covered graphs do not
+          contain zero loops.
+
+        EXAMPLES:
+
+        A matching covered graph, for instance the Truncated biwheel graph,
+        by definition, is always free of loops::
+
+            sage: T = graphs.TruncatedBiwheelGraph(5)
+            sage: G = MatchingCoveredGraph(T)
+            sage: G
+            Matching covered truncated biwheel graph: graph on 10 vertices
+            sage: G.has_loops()
+            False
+            sage: G.allows_loops()
+            False
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        A matching covered graph may support multiple edges, still no
+        loops are allowed::
+
+            sage: B = graphs.BiwheelGraph(4)
+            sage: G = MatchingCoveredGraph(B)
+            sage: G.allow_multiple_edges(True)
+            sage: G
+            Matching covered biwheel graph: multi-graph on 8 vertices
+            sage: G.add_edge(0, 1, 'label')
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label'), (0, 5, None), (0, 7, None),
+             (1, 2, None), (1, 6, None), (2, 3, None), (2, 7, None),
+             (3, 4, None), (3, 6, None), (4, 5, None), (4, 7, None),
+             (5, 6, None)]
+            sage: G.allows_loops()
+            False
+            sage: G.has_loops()
+            False
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
+        """
+        return 0
 
     @doc_index('Overwritten methods')
     def remove_loops(self, vertices=None):

From d24784855e9dac71a2b0bb0c166a165fa93f2569 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:28:54 +0530
Subject: [PATCH 07/19] Overwrote remove_loops()

---
 src/sage/graphs/matching_covered_graph.py | 92 ++++++++++++++++++++++-
 1 file changed, 91 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 77b3654374c..7d035d2de81 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2356,7 +2356,97 @@ def number_of_loops(self):
 
     @doc_index('Overwritten methods')
     def remove_loops(self, vertices=None):
-        raise NotImplementedError()
+        r"""
+        Remove loops on vertices in ``vertices``.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.generic_graph.GenericGraph.remove_loops` method
+            in order to return without any alteration as matching covered
+            graphs are free of looped edges.
+
+        INPUT:
+
+        - ``vertices`` -- (default: ``None``) iterator container of vertex
+          labels correponding to which the looped edges are to be removed. If
+          ``vertices`` is ``None``, remove all loops.
+
+        OUTPUT:
+
+        - Nothing is returned, as a matching covered graph is already devoid of
+          any loops.
+
+        EXAMPLES:
+
+        A matching covered graph, for instance the Wheel graph of order six, is
+        always free of loops::
+
+            sage: W = graphs.WheelGraph(6)
+            sage: G = MatchingCoveredGraph(W)
+            sage: G
+            Matching covered wheel graph: graph on 6 vertices
+            sage: G.has_loops()
+            False
+            sage: G.allows_loops()
+            False
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+            sage: G.remove_loops()
+            sage: G.edges(sort=True)
+            [(0, 1, None), (0, 2, None), (0, 3, None), (0, 4, None),
+             (0, 5, None), (1, 2, None), (1, 5, None), (2, 3, None),
+             (3, 4, None), (4, 5, None)]
+
+        A matching covered graph may support multiple edges, still no
+        loops are allowed::
+
+            sage: K = graphs.CompleteGraph(2)
+            sage: G = MatchingCoveredGraph(K)
+            sage: G.allow_multiple_edges(True)
+            sage: G
+            Matching covered complete graph: multi-graph on 2 vertices
+            sage: G.add_edge(0, 1, 'label')
+            sage: G.add_edge(0, 0)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label')]
+            sage: G.allows_loops()
+            False
+            sage: G.has_loops()
+            False
+            sage: G.loops()
+            []
+            sage: G.loop_edges()
+            []
+            sage: G.loop_vertices()
+            []
+            sage: G.number_of_loops()
+            0
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`
+        """
+        return
 
     @doc_index('Miscellaneous methods')
     def update_matching(self, matching):

From 369eeba7cf4ccf43e34c175202c1c8fa35b20f35 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:29:39 +0530
Subject: [PATCH 08/19] updated allow_loops()

---
 src/sage/graphs/matching_covered_graph.py | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 7d035d2de81..5f5cfbe8a26 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1622,6 +1622,16 @@ def allow_loops(self, new, check=True):
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allows_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
         """
         if new:
             raise ValueError('loops are not allowed in '

From cca3d4553aaf43561cfc88474bcdb26be42a9ea6 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 18:30:11 +0530
Subject: [PATCH 09/19] updated allows_loops()

---
 src/sage/graphs/matching_covered_graph.py | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 5f5cfbe8a26..66dfd8bc072 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1663,6 +1663,16 @@ def allows_loops(self):
             sage: G = MatchingCoveredGraph(P)
             sage: G.allows_loops()
             False
+
+        .. SEEALSO::
+
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.has_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_edges`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loop_vertices`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
+            :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
         """
         return False
 

From 0a88de6e80e1533dbd8b93fc5cc4c5cecedf058d Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:02:49 +0530
Subject: [PATCH 10/19] updated remove_loops()

---
 src/sage/graphs/matching_covered_graph.py | 28 +++++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 66dfd8bc072..8b615310e4b 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2455,6 +2455,28 @@ def remove_loops(self, vertices=None):
             []
             sage: G.number_of_loops()
             0
+            sage: G.remove_loops(vertices=[0, 1])
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label')]
+            sage: G.remove_loops(vertices=[0..100])
+
+        Note that the parameter ``vertices`` must be either ``None`` or an
+        iterable::
+
+            sage: G.remove_loops(vertices='')
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label')]
+            sage: G.remove_loops(vertices=None)
+            sage: G.edges(sort=False)
+            [(0, 1, None), (0, 1, 'label')]
+            sage: G.remove_loops(vertices=0)
+            Traceback (most recent call last):
+            ...
+            TypeError: 'Integer' object is not iterable
+            sage: G.remove_loops(vertices=False)
+            Traceback (most recent call last):
+            ...
+            TypeError: 'bool' object is not iterable
 
         .. SEEALSO::
 
@@ -2466,6 +2488,12 @@ def remove_loops(self, vertices=None):
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`
         """
+        from collections.abc import Iterable
+
+        if vertices is not None and not isinstance(vertices, Iterable):
+            raise TypeError(f'\'{vertices.__class__.__name__}\' '
+                            'object is not iterable')
+
         return
 
     @doc_index('Miscellaneous methods')

From d78f6043e78bfbf056cdd2af524d8cb67eb02dd9 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:03:28 +0530
Subject: [PATCH 11/19] corrected a typo

---
 src/sage/graphs/matching_covered_graph.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 8b615310e4b..e646667d4c7 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1936,7 +1936,7 @@ def get_matching(self):
     @doc_index('Overwritten methods')
     def has_loops(self):
         r"""
-        Check whether thare are loops in the (matching covered) graph.
+        Check whether there are loops in the (matching covered) graph.
 
         .. NOTE::
 

From cc07061dbda58513dfeae89e7c40c7e4ae961824 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:06:47 +0530
Subject: [PATCH 12/19] corrected the indentation

---
 src/sage/graphs/matching_covered_graph.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index e646667d4c7..77c461df37e 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2116,8 +2116,8 @@ def loop_edges(self, labels=True):
 
         INPUT:
 
-        - ``labels`` -- boolean (default: ``True``); whether returned edges have
-         labels (``(u,v,l)``) or not (``(u,v)``)
+        - ``labels`` -- boolean (default: ``True``); whether returned edges
+          have labels (``(u,v,l)``) or not (``(u,v)``).
 
         OUTPUT:
 

From e98aae7f87e900328300dbbd819f4cb44f4b6a97 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:14:57 +0530
Subject: [PATCH 13/19] updated the indentation

---
 src/sage/graphs/matching_covered_graph.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 77c461df37e..0d482cf23b6 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2013,7 +2013,6 @@ def has_loops(self):
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
-
         """
         return False
 
@@ -2200,7 +2199,7 @@ def loop_edges(self, labels=True):
 
     @doc_index('Overwritten methods')
     def loop_vertices(self):
-        """
+        r"""
         Return a list of vertices with loops.
 
         .. NOTE::
@@ -2282,7 +2281,6 @@ def loop_vertices(self):
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.loops`,
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.number_of_loops`,
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.remove_loops`
-
         """
         return []
 

From 327222716590b5c4120d7808ad458058820f8c7b Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:17:06 +0530
Subject: [PATCH 14/19] updated the doctest of loop_edges()

---
 src/sage/graphs/matching_covered_graph.py | 16 ----------------
 1 file changed, 16 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 0d482cf23b6..7550455ae7c 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2133,10 +2133,6 @@ def loop_edges(self, labels=True):
             sage: G = MatchingCoveredGraph(H)
             sage: G
             Matching covered heawood graph: graph on 14 vertices
-            sage: G.has_loops()
-            False
-            sage: G.allows_loops()
-            False
             sage: G.add_edge(0, 0)
             Traceback (most recent call last):
             ...
@@ -2145,10 +2141,6 @@ def loop_edges(self, labels=True):
             []
             sage: G.loop_edges()
             []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
 
         A matching covered graph may support multiple edges, still no
         loops are allowed::
@@ -2165,18 +2157,10 @@ def loop_edges(self, labels=True):
             ValueError: loops are not allowed in matching covered graphs
             sage: G.edges(sort=False)
             [(0, 1, None), (0, 1, 'label'), (0, 3, None), (1, 2, None), (2, 3, None)]
-            sage: G.allows_loops()
-            False
-            sage: G.has_loops()
-            False
             sage: G.loops()
             []
             sage: G.loop_edges()
             []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
 
         One may set the ``label`` to either ``True`` or ``False``::
 

From 023b05a43ae12b566b4f6df4a3672a311a817ec1 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:18:29 +0530
Subject: [PATCH 15/19] updated the doctest of loop_vertices()

---
 src/sage/graphs/matching_covered_graph.py | 20 --------------------
 1 file changed, 20 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 7550455ae7c..23038b1e139 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2208,22 +2208,12 @@ def loop_vertices(self):
             sage: G = MatchingCoveredGraph(M)
             sage: G
             Matching covered moebius ladder graph: graph on 8 vertices
-            sage: G.has_loops()
-            False
-            sage: G.allows_loops()
-            False
             sage: G.add_edge(0, 0)
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
             sage: G.loop_vertices()
             []
-            sage: G.number_of_loops()
-            0
 
         A matching covered graph may support multiple edges, still no
         loops are allowed::
@@ -2243,18 +2233,8 @@ def loop_vertices(self):
              (1, 2, None), (1, 4, None), (2, 5, None), (2, 7, None),
              (3, 4, None), (3, 6, None), (4, 5, None), (5, 7, None),
              (6, 7, None)]
-            sage: G.allows_loops()
-            False
-            sage: G.has_loops()
-            False
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
             sage: G.loop_vertices()
             []
-            sage: G.number_of_loops()
-            0
 
         .. SEEALSO::
 

From a2b4a9df9bef88b01d1a8aee4f246c96584176e4 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:19:24 +0530
Subject: [PATCH 16/19] updated the doctest of number_of_loops()

---
 src/sage/graphs/matching_covered_graph.py | 16 ----------------
 1 file changed, 16 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 23038b1e139..03cb4915d4f 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2276,18 +2276,10 @@ def number_of_loops(self):
             sage: G = MatchingCoveredGraph(T)
             sage: G
             Matching covered truncated biwheel graph: graph on 10 vertices
-            sage: G.has_loops()
-            False
-            sage: G.allows_loops()
-            False
             sage: G.add_edge(0, 0)
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
             sage: G.loop_vertices()
             []
             sage: G.number_of_loops()
@@ -2311,14 +2303,6 @@ def number_of_loops(self):
              (1, 2, None), (1, 6, None), (2, 3, None), (2, 7, None),
              (3, 4, None), (3, 6, None), (4, 5, None), (4, 7, None),
              (5, 6, None)]
-            sage: G.allows_loops()
-            False
-            sage: G.has_loops()
-            False
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
             sage: G.loop_vertices()
             []
             sage: G.number_of_loops()

From ca0f5cc9979691ac78a36dac3c037e0fca822f1e Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:20:14 +0530
Subject: [PATCH 17/19] updated the doctest of remove_loops()

---
 src/sage/graphs/matching_covered_graph.py | 24 -----------------------
 1 file changed, 24 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 03cb4915d4f..6d4bb1ff439 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -2352,22 +2352,10 @@ def remove_loops(self, vertices=None):
             sage: G = MatchingCoveredGraph(W)
             sage: G
             Matching covered wheel graph: graph on 6 vertices
-            sage: G.has_loops()
-            False
-            sage: G.allows_loops()
-            False
             sage: G.add_edge(0, 0)
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
             sage: G.remove_loops()
             sage: G.edges(sort=True)
             [(0, 1, None), (0, 2, None), (0, 3, None), (0, 4, None),
@@ -2389,18 +2377,6 @@ def remove_loops(self, vertices=None):
             ValueError: loops are not allowed in matching covered graphs
             sage: G.edges(sort=False)
             [(0, 1, None), (0, 1, 'label')]
-            sage: G.allows_loops()
-            False
-            sage: G.has_loops()
-            False
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
             sage: G.remove_loops(vertices=[0, 1])
             sage: G.edges(sort=False)
             [(0, 1, None), (0, 1, 'label')]

From 6fe61f8382e355e93c9e38832e21c07c44d4496e Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 19:21:51 +0530
Subject: [PATCH 18/19] updated the doctest of has_loops()

---
 src/sage/graphs/matching_covered_graph.py | 22 +++++-----------------
 1 file changed, 5 insertions(+), 17 deletions(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 6d4bb1ff439..86bb5148378 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1967,14 +1967,6 @@ def has_loops(self):
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
 
         A matching covered graph may support multiple edges, still no
         loops are allowed::
@@ -1995,15 +1987,11 @@ def has_loops(self):
             False
             sage: G.has_loops()
             False
-            sage: G.loops()
-            []
-            sage: G.loop_edges()
-            []
-            sage: G.loop_vertices()
-            []
-            sage: G.number_of_loops()
-            0
-
+            sage: G.allow_loops(True)
+            Traceback (most recent call last):
+            ...
+            ValueError: loops are not allowed in matching covered graphs
+            
         .. SEEALSO::
 
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,

From d8beed1bb7aa8860c2e9e009e31c0d428f5fd350 Mon Sep 17 00:00:00 2001
From: janmenjayap <janmenjaya.panda.22@gmail.com>
Date: Sun, 10 Nov 2024 20:52:49 +0530
Subject: [PATCH 19/19] removed whitespaces from a blankline

---
 src/sage/graphs/matching_covered_graph.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/graphs/matching_covered_graph.py b/src/sage/graphs/matching_covered_graph.py
index 86bb5148378..2732e0b46a5 100644
--- a/src/sage/graphs/matching_covered_graph.py
+++ b/src/sage/graphs/matching_covered_graph.py
@@ -1991,7 +1991,7 @@ def has_loops(self):
             Traceback (most recent call last):
             ...
             ValueError: loops are not allowed in matching covered graphs
-            
+
         .. SEEALSO::
 
             :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.allow_loops`,