The largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)

Abstract

Let S 1 (m, d, k) be the k-uniform supertree obtained from a loose path P :. Let S(m, d, k) be the set of k-uniform supertrees with m edges and diameter d and q(G) be the signless Laplacian spectral radius of a k-uniform hypergraph G. In this paper, we mainly determine S 1 (m, d, k) with the largest signless Laplacian spectral radius among all supertrees in S(m, d, k) for 3 ≤ d ≤ m − 1. Furthermore, we determine the unique uniform supertree with the maximum signless Laplacian spectral radius among all the uniform supertrees with n vertices and pendent edges (vertices).