Graph isomorphism recognition using scheme matrices

Abstract

The issue of isomorphism graphs recognition is as follows: whether there is a polynomial algorithm that recognizes isomorphism of each pair of graphs. The issue of isomorphism recognition is one of the most important in the graph theory and belongs to the class of NP-complete problems which includes problems for which polynomial algorithms are unknown. Despite numerous attempts, the problem of verifying the isomorphism of graphs belongs to those ones that cannot be classified according to their complexity. The issue of computational complexity of the problem remains open, although for some special cases efficient algorithms with polynomial computational complexity have been constructed. The paper develops and justifies a graph isomorphism recognition method whose computational complexity is polynomial.