Some spectral properties of uniform hypergraphs

Abstract

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that ∑ni=1 dsi (s=1,…,k) is determined by the Laplacian spectrum of H, where d1,…,dn is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al (2014). We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al (2013) holds under certain conditons.