Product graph representations

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(log2n) time. © 1929 John Wiley & Sons, Inc.

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