An optimized algorithm for the identification of isomorphic undirected graphs

Abstract

This paper presents an approach to graph isomorphism identification. The approach is an optimized version of the circuit simulation method, which we proposed in one previous paper. Both the optimized and the original methods solve the graph isomorphism problem through circuit modeling and simulation. The simulation result, a series of node voltages, is taken as the identification index for a graph and isomorphism is determined by comparing the indices of two graphs. In general, circuit simulation needs a reference node. In the original method, each vertex takes turns to serve as reference, which leads to inconvenience and complexity in computation; in the optimized version, an extra vertex is added to the graph to work as a reference node in the circuit, which simplifies computation and the form of identification index, thus enhancing the efficiency. Both methods are tested on a large number of random undirected graphs generated by the computer and the experiment result shows that the runtime of the optimized method is much lower than that of the original one.