Square Property, Equitable Partitions, and Product-like Graphs
arXiv:1301.6898 · doi:10.1016/j.disc.2013.12.012
Abstract
Equivalence relations on the edge set of a graph that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of , which in turn give rise to quotient graphs that can have a rich product structure even if itself is prime.
20 pages, 6 figures