Maximization of the spectral radius of block graphs with a given dissociation number

Abstract

A connected graph is called a block graph if each of its blocks is a complete graph. Let Bl(k,φ) be the class of block graphs on k vertices with given dissociation number φ. In this article, we have shown the existence and uniqueness of a block graph Bk,φ in Bl(k,φ) that maximizes the spectral radius ρ(G) among all graphs G in Bl(k,φ). Furthermore, we also provide bounds on ρ(Bk,φ).