Parallel graph isomorphism detection with identification matrices

Abstract

In this paper, we investigate some properties of identification matrices and exhibit some uses of identification matrices in studying the graph isomorphism problem, a well-known long-standing open problem. We show that, given two m/spl times/n identification matrices representing two graphs according to a certain relation, isomorphism can be decided efficiently in parallel if an m/spl times/(n-c) submatrix, for a constant c, satisfies the consecutive/circular 1's property. The result presented here significantly broadens the class of graphs for which there are known efficient parallel isomorphism testing algorithms.<>