Algorithms for finding directed graph isomorphisms by finite automata

Abstract

The determination of the isomorphisms between two directed graphs based on those between the corresponding one-input Moore machines plus an additional condition to be checked is developed. Without this condition, the Moore machine isomorphism problem is not equivalent to the graph isomorphism problem. Two algorithms are devised for solving the graph isomorphism problem based on the above method. These algorithms are implemented aspl/1 programs, executed on an IBM System 370/158, experimentally analyzed by a random graph generating program and abal assembly language time routine, and illustrated by examples. The experimental data for the class of isomorphicn/2 regular graphs are fitted by quadratic equations of the input size. In addition the worst-case complexities of both algorithms are found.