Bounds on the Aα-spectral radius of uniform hypergraphs with some vertices deleted

Abstract

Let $D\left(G\right)$ and $A\left(G\right)$ be the diagonal and adjacency tensors of a $k$-uniform hypergraph $G,$ respectively. The $A_{\alpha }$-spectral radius of $G$ is defined as the spectral radius of the tensor $A_{\alpha }\left(G\right)=\alpha D\left(G\right)+(1-\alpha )A\left(G\right),$ where $0\le \alpha <1.$ In this paper, we obtain an interlacing inequality on the spectral radius of a principal subtensor for a nonnegative weakly irreducible symmetric tensor, which is used to present several sharp lower bounds for the $A_{\alpha }$-spectral radius of any subhypergraph $G-S$ of a connected $k$-uniform hypergraph $G$ in terms of the principal eigenvector associated with the $A_{\alpha }$-spectral radius of $G$, degrees and co-degrees, where $S$ is a subset of $V\left(G\right)$. They extend and strengthen some known results.