The (signless Laplacian) spectral radius (of subgraphs) of uniform hypergraphs

Abstract

Let $\lambda_{1}(G)$ and $q_{1}(G)$ be the spectral radius and the signless Laplacian spectral radius of a $k$-uniform hypergraph $G$, respectively. In this paper, we give the lower bounds of $d-\lambda_{1}(H)$ and $2d-q_{1}(H)$, where $H$ is a proper subgraph of a $f$(-edge)-connected $d$-regular (linear) $k$-uniform hypergraph.  Meanwhile, we also give  the lower bounds of $2\Delta-q_{1}(G)$ and $\Delta-\lambda_{1}(G)$, where $G$ is an irregular $f$(-edge)-connected (linear) $k$-uniform hypergraph with maximum degree $\Delta$. Some of these results extend the results of Shiu, Huang and Sun from graphs to $k$-uniform hypergraphs.