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:

IsomorphicGraphQ works with undirected graphs:

Directed graphs:

IsomorphicGraphQ gives False for non-isomorphic graphs:

As well as non-graph expressions:

IsomorphicGraphQ works with 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: