Structure based algorithm for solving Graph Isomorphism for Johnson, Generalised Johnson and Strongly Regular graphs

Abstract

Graph Isomorphism has been reduced to quasi-polynomial time complexity by Laszlo Babai. However, his solution is not extendable to extremely symmetric Johnson graphs. A method to reduce the runtime complexity of Graph Isomorphism to polynomial space would have wide ranging effects. We have identified and implemented a way to solve Graph Isomorphism for Johnson, Generalised Johnson and Strongly Regular graphs. The method is based on structural organisation in terms of participation of vertices of a graph in formation of cyclical shapes of specific order. The method successfully identifies isomorphs among Johnson, Generalised Johnson and Strongly Regular graphs with polynomial time complexity. Such methods will eventually significant advancements in the field of cryptography, automata theory, compilers, image processing etc.