This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# IsomorphicGraphQ

 IsomorphicGraphQ yields True if the graphs and are isomorphic, and False otherwise.
• Two graphs are isomorphic if there is a renaming of vertices that makes them equal.
Test whether two graphs are isomorphic:
Find an isomorphism that maps g to h:
Renaming the vertices of graph g gets an equal graph as h:
Test whether two graphs are isomorphic:
 Out[2]=
Find an isomorphism that maps g to h:
 Out[3]=
Renaming the vertices of graph g gets an equal graph as h:
 Out[4]=
 Scope   (4)
Test undirected graphs:
Test directed graphs:
IsomorphicGraphQ gives False for non-isomorphic graphs:
As well as non-graph expressions:
Test large graphs:
Isomorphic graphs have the same number of vertices and edges:
The isomorphic graphs have the same ordered degree sequence:
The graphs with the same degree sequence can be non-isomorphic:
FindGraphIsomorphism can be used to find the mapping between vertices:
Highlight and label two graphs according to the mapping:
Permuting the vertices in a graph produces an isomorphic graph:
The graph generated by the permutation of its adjacency matrix is isomorphic to itself:
Sample a permutation of the vertex list:
The line graph of a cycle graph is isomorphic to itself:
The line graph of a path is isomorphic to :
The complement of the line graph of is isomorphic to a Petersen graph:
Two connected graphs are isomorphic iff their line graphs are isomorphic:
With one exception:
The non-isomorphic directed graphs can have undirected graphs that are isomorphic:
New in 8