Refined Vertex Codes and Vertex Partitioning Methodology for Graph Isomorphism Testing

In this paper we have pursued the initial vertex partioning methodology for a graph (digraph) isomorphism testing problem using lexicographic ordering of vertex codes. The newly introduced vertex codes (which may be of fixed length or of variable length) incorporate order independent parameters of a graph in relation to a vertex and can be computed efficiently. The vertex partitioning obtaned by the lexicographic ordering of vertex codes is shown to yield the most refined initial vertex partioning known. Examples are presented for the illustration of our method. Specifically, we demonstrate that our approach of using refined vertex oodes for vertex partitioning indeed distinguishes the nonisomorphic cases of strongly regular gaphs of 28 vertices. Our results suggest that the methodology Is powerful in the context of isomorphism testing for large classes of graphs. Further research needed in this area is indicated.