Bounds for the incidence Q-spectral radius of uniform hypergraphs

Abstract

The incidence $Q$-spectral radius of a k-uniform hypergraph G with n vertices and m edges is defined as the spectral radius of the incidence $Q$-tensor $Q^{⁎}:=RI{R}^T$, where R is the incidence matrix of G, and $I$ is an order k dimension m identity tensor. Since the $(i_1,i_2,\dots ,i_k)$-entry of $Q^{⁎}$ is involved in the number of edges in G containing vertices $i_1,i_2,\dots ,i_k$ simultaneously, more structural properties of G from the entry of $Q^{⁎}$ than other commonly used tensors associated with hypergraphs may be discovered. In this paper, we present several bounds on the incidence $Q$-spectral radius of G in terms of degree sequences, which are better than some known results in some cases.