Parallel graph isomorphism detection with identification matrices

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×n identification matrices representing two graphs according to a certain relation, isomorphism can be decided efficiently in parallel if an m×(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