On Extremal Spectral Radii of Uniform Supertrees with Given Independence Number

Abstract

A supertree is a connected and acyclic hypergraph. Denote by Tm,n,α the set of m-uniform supertrees of order n with independent number α. Focusing on the spectral radius in Tm,n,α, this present completely determines the hypergraphs with maximum spectral radius among all the supertrees with n vertices and independence number α for m−1/mn≤α≤n−1, which extend the results of Lu et al. from tree to uniform supertree. Our techniques are based on the structure properties of supertrees with given independence number and general edge-moving operation. As a byproduct, we also determine the hypergraphs with minimum signless Laplacian spectral radius in Tm,n,α.