On the spectral radius of block graphs with prescribed independence number α

Abstract

Let G(n,α) be the class of block graphs on n vertices and prescribed independence number α. In this article we prove that the maximum spectral radius ρ(G), among all graphs G∈G(n,α), is reached at a unique graph. As a byproduct we obtain an upper for ρ(G), when G∈G(n,α).