The inner power of a graph
Richard H. Hammack, Neal Livesay · Ars Mathematica Contemporanea · 2010
We define a new graph operation called the k th inner power . The construction—which is somewhat analogous to the k th 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.