The Spectral Relation between the Cube-Connected Cycles and the Shuffle-Exchange Network

Abstract

We investigate the relation between the spectral sets (i. e., the sets of eigenvalues, disregarding multiplicities) of two d-dimensional networks popular in parallel computing: the Cube-Connected Cycles network CCC(d) and the Shuffle-Exchange network SE(d). We completely characterize their spectral sets. Additionally, it turns out that for any odd d, the SE(d)-eigenvalues set is precisely the same as the CCC(d)eigenvalues set. For any even d, however, the SE(d)-eigenvalues form a proper subset of the set of CCC(d)-eigenvalues.