Proof of a conjecture on distance energy of complete multipartite graphs

Abstract

Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009), G-2009-64] derived certain spectral properties of the distance matrix of complete multipartite graphs, and conjectured that the distance energy of a complete multipartite graph on n vertices having γ parts, each of size at least two, is equal to 4(n-γ). We prove this conjecture.