The spectrum of a class of uniform hypergraphs

A generalized power hypergraph Hsk is obtained from a base hypergraph H by means of some simple edge-expansion operations. Kang, Liu, Qi and Yuan [8] proved that the nonzero eigenvalues of H give rise to nonzero eigenvalues of Hsk. In this paper we show that all nonzero eigenvalues of Hsk may be computed from the eigenvalues of its base hypergraph H and of its subgraphs. To prove this, we derive spectral results about edge-expansion operations that may be interesting on their own sake.