Introduction

Abstract

The graph isomorphism problem consists in deciding whether two given graphs are isomorphic, i.e. whether there is a bijective mapping (a permutation) from the nodes of one graph to the nodes of the second graph such that the edge connections are respected. The problem is of considerable practical, as well as theoretical, importance. Many isomorphism problems for other combinatorial structures can be considered as special cases of the graph isomorphism problem. However, until today, this problem is still unresolved in the sense that no efficient algorithm for it has yet been found. On the other hand, no NP-completeness proof for graph isomorphism, nor any other arguments for its intractability have been obtained either.