Product graph representations

Abstract

We study a hierarchy of canonical representations of grpahs as subgraphs of cartesian products of graphs. This hierarchy starts with the isometric representation, includes the 2‐isometric represnetation, and ends with the cartesian prime factorization. We show that all three representations can be obtained in O(nm) time using O(m) space, for graphs with n vertices and m edges. The algorithms have immediate parallel versions that use n3 processors and run in O(log2 n) time. © 1929 John Wiley & Sons, Inc. Copyright © 1992 Wiley Periodicals, Inc., A Wiley Company