The spectral relation between the cube-connected cycles and the shuffle-exchange network
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.
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