The characteristic polynomial of the complete 3-uniform hypergraph

Abstract

In this paper, we give the characteristic polynomial of the complete 3-uniform hypergraph. We show that the characteristic polynomial is the product of some cubic polynomials, so we can easily compute the spectra of complete 3-uniform hypergraphs. This computation includes a complete description of the eigenvalues' multiplicities. We also show the algebraic multiplicities of 0, 1 and (n−12) of a complete 3-uniform hypergraph with n vertices.