On Extremal Spectral Radii of Uniform Supertrees with Given Independence Number

Abstract

A supertree is a connected and acyclic hypergraph. Denote by T m , n , α the set of m -uniform supertrees of order n with independent number α . Focusing on the spectral radius in T m , 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 / m n ≤ 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 T m , n , α .