On the distance energy of k-uniform hypergraphs

Abstract

Abstract In this article, we extend the concept of distance energy for hypergraphs. We first establish a relation between the distance energy and the distance spectral radius. Then, we obtain some bounds for the distance energy in terms of some invariant of hypergraphs such as the determinant of the distance matrix, number of vertices, and Wiener index along with the distance energy of join of k k -uniform hypergraphs. Furthermore, it is shown that the determinant of the distance matrix of k k -uniform hyperstar on n n vertices is ( − 1 ) n − 1 ( n − 1 ) k n − k k − 1 {\left(-1)}^{n-1}\left(n-1){k}^{\tfrac{n-k}{k-1}} . Later, the distance spectrum of k k -uniform hyperstar is obtained, which gives the explicit distance energy of k k -uniform hyperstar.