Some conjectures and properties on distance energy

Abstract

The distance energy of a graph G is defined as \(ED(G) = \sum |\mu_i|\)|, where µi is the ith eigenvalue of the distance matrix of G. In this paper, we express the distance spectra and distance energy of complete split graphs and graphs composed of two cliques joined by a matching. We also give some spectral properties of complete multipartite graphs. Finally, we identify structural and numerical conjectures on ED for graphs with number of vertices n and number of edges m are fixed.