On the distance energy of k-uniform hypergraphs

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 kk-uniform hypergraphs. Furthermore, it is shown that the determinant of the distance matrix of kk-uniform hyperstar on nn vertices is (−1)n−1(n−1)kn−kk−1{\left(-1)}^{n-1}\left(n-1){k}^{\tfrac{n-k}{k-1}}. Later, the distance spectrum of kk-uniform hyperstar is obtained, which gives the explicit distance energy of kk-uniform hyperstar.

Keywords

• hypergraph
• distance matrix
• distance degree
• spectral radius
• distance energy
• hyperstar
• 05c15
• 05c50
• 05c65
• 15a18