# HG changeset patch
# User Nathann Cohen <nathann.cohen@gmail.com>
# Date 1299590088 3600
# Node ID 7c3d566411e2dc69f5ff9f9c56d67b5570769f27
# Parent 3a67c2a91eeb21a93364f7caa9e8fe7945d4def6
#10781  Shrikhande graph to the common graphs database (reviewer patch)
diff r 3a67c2a91eeb r 7c3d566411e2 sage/graphs/graph_generators.py
a

b


3486  3486  """ 
3487  3487  Returns the Shrikhande graph. 
3488  3488  
3489   For more information, see `this MathWorld article on the Shrikhande graph <http://mathworld.wolfram.com/ShrikhandeGraph.html>`_ or 
3490   `this Wikipedia article <http://en.wikipedia.org/wiki/Shrikhande_graph>`_. 
 3489  For more information, see `this MathWorld article on the Shrikhande 
 3490  graph <http://mathworld.wolfram.com/ShrikhandeGraph.html>`_ or `this 
 3491  Wikipedia article <http://en.wikipedia.org/wiki/Shrikhande_graph>`_. 
3491  3492  
3492  3493  EXAMPLES: 
3493  3494  
3494   The Shrikhande graph was defined by S. S. Shrikhande in 1959. It has 16 vertices and 48 edges, and is strongly regular of degree 6 with parameters (2,2):: 
 3495  The Shrikhande graph was defined by S. S. Shrikhande in 1959. It has 
 3496  `16` vertices and `48` edges, and is strongly regular of degree `6` with 
 3497  parameters `(2,2)`:: 
3495  3498  
3496  3499  sage: G = graphs.ShrikhandeGraph(); G 
3497  3500  Shrikhande graph: Graph on 16 vertices 
… 
… 

3501  3504  48 
3502  3505  sage: G.is_regular(6) 
3503  3506  True 
3504   sage: set([len([x for x in G.neighbors(i) if x in G.neighbors(j)]) for i in range(G.order()) for j in range(i)]) 
 3507  sage: set([len([x for x in G.neighbors(i) if x in G.neighbors(j)]) 
 3508  ... for i in range(G.order()) 
 3509  ... for j in range(i)]) 
3505  3510  set([2]) 
3506  3511  
3507  3512  It is nonplanar, and both Hamiltonian and Eulerian:: 
… 
… 

3513  3518  sage: G.is_eulerian() 
3514  3519  True 
3515  3520  
3516   It has radius 2, diameter 2, and girth 3:: 
 3521  It has radius `2`, diameter `2`, and girth `3`:: 
3517  3522  
3518  3523  sage: G.radius() 
3519  3524  2 
… 
… 

3522  3527  sage: G.girth() 
3523  3528  3 
3524  3529  
3525   Its chromatic number is 4 and its automorphism group is of order 192:: 
 3530  Its chromatic number is `4` and its automorphism group is of order 
 3531  `192`:: 
3526  3532  
3527  3533  sage: G.chromatic_number() 
3528  3534  4 