Incidence Energy of k-Uniform Hypertrees

Abstract

For a square matrix M, its energy E(M) is the sum of its singular values. Let H be a k-uniform hypergraph, and let B(H) be the incidence matrix of H. The incidence energy BE(H) of H is the energy of B(H). Let T n,d be the set of k-uniform hypertrees of order n and size r with diameter 3 ≤ d ≤ r − 1. In this article, the k-uniform hypertrees with minimum incidence energy over T n,d are characterized. In addition, we have obtained the incidence energy of a hyperstar, and determined which hyperstar has the maximum and minimum incidence energy among all hyperstars with n vertices.