Ticket #13709: trac_13709.patch

sage/graphs/generators/smallgraphs.py

@@ -2202 +2202 @@
 
     REFERENCES:
 
-    - [1] Godsil, C. and Royle, G. Algebraic Graph Theory.
+    .. [GodsilRoyle] Godsil, C. and Royle, G. Algebraic Graph Theory.
       Springer, 2001.
 
     EXAMPLES::
@@ -2699 +2699 @@
     P.name("Petersen graph")
     return P
 
+def SchlaefliGraph():
+    r"""
+    Returns the Schläfli graph.
+
+    The Schläfli graph is the only strongly regular graphs of parameters
+    `(27,16,10,8)` (see [GodsilRoyle]_).
+
+    For more information, see the :wikipedia:`Wikipedia article on the
+    Schläfli graph <Schläfli_graph>`.
+
+    .. SEEALSO::
+
+        :meth:`Graph.is_strongly_regular` -- tests whether a graph is strongly
+        regular and/or returns its parameters.
+
+    .. TODO::
+
+        Find a beautiful layout for this beautiful graph.
+
+    EXAMPLE:
+
+    Checking that the method actually returns the Schläfli graph::
+
+        sage: S = graphs.SchlaefliGraph()
+        sage: S.is_strongly_regular(parameters = True)
+        (27, 16, 10, 8)
+
+    The graph is vertex-transitive::
+
+        sage: S.is_vertex_transitive()
+        True
+
+    The neighborhood of each vertex is isomorphic to the complement of the
+    Clebsch graph::
+
+        sage: neighborhood = S.subgraph(vertices = S.neighbors(0))
+        sage: graphs.ClebschGraph().complement().is_isomorphic(neighborhood)
+        True
+    """
+    from sage.graphs.graph import Graph
+    G = Graph('ZBXzr|}^z~TTitjLth|dmkrmsl|if}TmbJMhrJX]YfFyTbmsseztKTvyhDvw')
+    order = [1,8,5,10,2,6,11,15,17,13,18,12,9,24,25,3,26,7,16,20,23,0,21,14,22,4,19]
+    _circle_embedding(G, order)
+    G.name("Schläfli graph")
+    return G
+
 def ShrikhandeGraph():
     """
     Returns the Shrikhande graph.
 
     For more information, see the `MathWorld article on the Shrikhande graph
-    <http://mathworld.wolfram.com/ShrikhandeGraph.html>`_ or the `Wikipedia
-    article on the Shrikhande graph
-    <http://en.wikipedia.org/wiki/Shrikhande_graph>`_.
+    <http://mathworld.wolfram.com/ShrikhandeGraph.html>`_ or the
+    :wikipedia:`Wikipedia article on the Shrikhande graph <Shrikhande_graph>`.
+
+    .. SEEALSO::
+
+        :meth:`Graph.is_strongly_regular` -- tests whether a graph is strongly
+        regular and/or returns its parameters.
 
     EXAMPLES:
 

sage/graphs/graph_generators.py

@@ -129 +129 @@
      "NauruGraph",
      "PappusGraph",
      "PetersenGraph",
+     "SchlaefliGraph",
      "ShrikhandeGraph",
      "ThomsenGraph",
      "Tutte12Cage",
@@ -719 +720 @@
         These will be simple graphs: no loops, no multiple edges, no
         directed edges.
 
+        .. SEEALSO::
+
+            :meth:`Graph.is_strongly_regular` -- tests whether a graph is
+            strongly regular and/or returns its parameters.
+
         EXAMPLES:
 
         The generator can be used to construct graphs for testing,
@@ -812 +818 @@
            cospectral graphs (lists of cadinality 1 being omitted).
 
 
+        .. SEEALSO::
+
+            :meth:`Graph.is_strongly_regular` -- tests whether a graph is
+            strongly regular and/or returns its parameters.
+
         EXAMPLES::
 
             sage: g=graphs.cospectral_graphs(5)
@@ -974 +985 @@
     NauruGraph               = staticmethod(sage.graphs.generators.smallgraphs.NauruGraph)
     PappusGraph              = staticmethod(sage.graphs.generators.smallgraphs.PappusGraph)
     PetersenGraph            = staticmethod(sage.graphs.generators.smallgraphs.PetersenGraph)
+    SchlaefliGraph           = staticmethod(sage.graphs.generators.smallgraphs.SchlaefliGraph)
     ShrikhandeGraph          = staticmethod(sage.graphs.generators.smallgraphs.ShrikhandeGraph)
     ThomsenGraph             = staticmethod(sage.graphs.generators.smallgraphs.ThomsenGraph)
     Tutte12Cage              = staticmethod(sage.graphs.generators.smallgraphs.Tutte12Cage)