The inner power of a graph

Richard H. Hammack, Neal Livesay


We define a new graph operation called the kth inner power. The construction—which is somewhat analogous to the kth power with respect to the direct product—seems to lend itself nicely to certain questions concerning cancellation over the direct product. We prove several results about bipartiteness and connectedness of inner powers, and we prove that the inner power distributes over the direct product. We explore a potential connection between inner powers and the problem of cancellation over the direct product.


Graph producs, graph operations, cancellation in graph products

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ISSN: 1855-3974

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