The IsIsomorphic command accepts two unweighted undirected graphs as input, and returns true if the graphs are isomorphic to each other, and false otherwise.

If a third argument phi is provided, it is assigned to a list of equations of the form v1=v2, where the v1 and v2 correspond to the vertices of graph 1 and graph 2 respectively, that provide a mapping of vertices that shows the graphs are isomorphic.

The method used is a backtracking algorithm that provides reasonable efficiency even for large graphs. (In general the the graph isomorphism problem is exponential in the number of vertices.)