On the α-spectral radius of the k-uniform supertrees

Abstract

Let [Formula: see text] be a [Formula: see text]-uniform hypergraph with vertex set [Formula: see text] and edge set [Formula: see text]. A connected and acyclic hypergraph is called a supertree. For [Formula: see text], the [Formula: see text]-spectral radius of [Formula: see text] is the largest [Formula: see text]-eigenvalue of [Formula: see text], where [Formula: see text] and [Formula: see text] are the diagonal tensor of the degrees and the adjacency tensor of [Formula: see text], respectively. In this paper, we determine the unique supertrees with maximum [Formula: see text]-spectral radius among all [Formula: see text]-uniform supertrees with [Formula: see text] edges and independence number [Formula: see text] for [Formula: see text], among all [Formula: see text]-uniform supertrees with given degree sequences, and among all [Formula: see text]-uniform supertrees with [Formula: see text] edges and matching number [Formula: see text] for [Formula: see text], respectively.