Implemented generators for some small graphs/ digraphs

src/doc/en/reference/references/index.rst

@@ -1704,6 +1704,11 @@ REFERENCES:
 .. [CLG1997] Frank Celler and C. R. Leedham-Green,
              *Calculating the Order of an Invertible Matrix*, 1997
 
+.. [CLM2006] Marcelo H. de Carvalho, Cláudio L. Lucchesi and U.S.R. Murty,
+             *How to build a brick*, Discrete Mathematics, Volume 306,
+             Issues 19--20, Pages 2383--2410,ISSN 0012--365X, (2006),
+             :doi:`10.1016/j.disc.2005.12.032`.
+
 .. [CLRS2001] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
               and Clifford Stein, *Section 22.4: Topological sort*,
               Introduction to Algorithms (2nd ed.), MIT Press and

src/sage/graphs/generators/smallgraphs.py

@@ -3828,8 +3828,87 @@ def MoserSpindle():
 def MurtyGraph():
     r"""
     Return the Murty graph.
+
+    Consider the complete bipartite graph `K_{3, 3}`. There is a set of three
+    black vertices and a set of three white vertices. Now, consider splicing
+    the complete graph `K_4` with one of the black vertices, this generates the
+    graph `K_4 \odot K_{3, 3}`. The Murty graph is obtained from
+    `K_4 \odot K_{3, 3}` with the addition of an edge joining the remaining two
+    black vertices. The Murty graph is free of conformal bicycles; in
+    other words, the Murty graph is an example of a graph that is Birkhoff-von
+    Neumann as well as PM-compact.
+
+    This is the smallest brick that is Birkhoff-von Neumann, aka a solid
+    brick, but is not odd-intercyclic. It is in this context that
+    Prof. U.S.R. Murty first stumbled upon this graph, and it also appears in
+    the work of Carvalho, Lucchesi, and Murty [CLM2006]_.
+
+    PLOTTING:
+
+    Upon construction, the position dictionary is filled to override
+    the spring-layout algorithm. By convention, the Murty graph is
+    displayed as mentioned in the paper [CKWL2019]_, with the first two
+    (noncubic) vertices on the top row, the second three vertices (that form a
+    stable set) in the middle row, and the remaining three vertices (that form
+    a triangle) at the bottom.
+
+    OUTPUT:
+
+    - ``G`` -- the Murty graph
+
+    EXAMPLES:
+
+    Construct and show the Murty graph::
+
+        sage: g = graphs.MurtyGraph()
+        sage: g.name()
+        'Murty Graph'
+        sage: g.order()
+        8
+        sage: g.size()
+        13
+        sage: g.girth()
+        3
+        sage: g.diameter()
+        2
+        sage: g.is_hamiltonian()
+        True
+        sage: g.show()                          # long time                             # needs sage.plot
+
+    REFERENCES:
+
+    - [CKWL2019]_
+    - [CLM2006]_
+    - [LM2024]_
+
+    AUTHORS:
+
+    - Janmenjaya Panda (2024-08-03)
     """
-    raise NotImplementedError()
+    pos_dict = {
+        0: (-0.5, sqrt(3)/2),
+        1: (0.5, sqrt(3)/2),
+        2: (-1, 0),
+        3: (0, 0),
+        4: (1, 0),
+        5: (-0.5, -1 - sqrt(3)/2),
+        6: (0, -1),
+        7: (0.5, -1 - sqrt(3)/2)
+    }
+
+    G = Graph(8, pos=pos_dict, name="Murty Graph")
+
+    G.add_edge(0, 1)
+    for v in range(2, 5):
+        G.add_edges([
+            (0, v), (1, v), (v, v+3)
+        ])
+
+    G.add_edges([
+        (5, 6), (5, 7), (6, 7)
+    ])
+
+    return G
 
 
 def NauruGraph(embedding=2):