On the spectra of k-uniform threshold hypergraphs

Abstract

In this article we introduce a definition of k-uniform thresholds hypergraphs through a binary sequence, a natural extension of the classical definition for thresholds graphs. We characterize some of its eigenvalues and multiplicities by means of combinatorial numbers, derived from edge counts. An important problem addressed in Spectral Graph Theory is to find graphs with few distinct eigenvalues. Our characterization allows us to construct k-uniform threshold hypergraphs having an arbitrary number of vertices with few distinct eigenvalues.