An efficient linear algebraic algorithm for the determination of isomorphism in pairs of undirected graphs

Abstract

An algorithm, complete with a spec ific FORTRAN implementation, is presented for the problem of determining whether or not two undirec tr d graphs are isomorphic. The algorithm, centered upon the eigenvalues and eigenvectors of a modified adjacency matrix and techniques for decreasing the size of the automorphism group, is quite different from others (mos t of which are comhinatorially based) and tends to work relatively very quickly on difficult tes t cases as well as on typical exa mples. Complexity estimates are given for many eventualities.