Initial vertex partitioning and testing isomorphism of graphs and digraphs

In this paper, we present a new method for initial vertex partitioning of graphs (digraphs) using the notion of a vertex label that includes several parameters of the graph for each vertex of the graph (digraph). Our method provides a more refined initial vertex partitioning for graphs (digraphs) than any of the known methods in O(nE) time for a graph with n vertices and E edges. Several examples are given as illustrations of the method. A computational comparison of our method with the Schmidt-Druffel algorithm is presented. The method can be coupled with any existing good back-tracking method for testing isomorphism of graphs and digraphs.

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