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 ${\sum }_{i=1}^n{d}_i^s$ ($s=1,\dots ,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\dots ,d_n$ 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 \cite{ShaoShanWu}. We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al \cite{HuQiShao} holds under certain conditons.

References in corpus (1)

• The extremal spectral radii of $k$-uniform supertrees