On 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 graph on k vertices with given dissociation number ϕ. In this article, we have obtained a block graph in Bl(k, ϕ) that uniquely attains the maximum spectral radius ρ(G) among all graphs G in Bl(k, ϕ).