The graph isomorphism problem

Abstract

Abstract A chemically and graph‐theoretically relevant problem is that of determining whether a pair of graphs G and G ′ are isomorphic. A two‐stage computational test is developed. In the first stage an “eigenvalue‐eigenprojector” tabular graph‐theoretic invariant is computed, whence if the two tables differ, G and G ′ must be nonisomorphic. The second stage, utilizing the tables of the first stage, orders the vertices, thereby leading to a special labeling for them, whence if the associated adjacency matrices for G and G ′ are equal, it must be that G and G ′ are isomorphic. The computational implementation, and testing of the algorithm is described.