A Simple Algorithm for a Computationally Hard Problem

Abstract: Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of n-vertex graphs whose adjacency matrices are not strongly co-det. Strongly co-det pair of matrices have very special symmetric structure which can be disarranged to be not strongly co-det by manipulating one element of the matrices.