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

Let G(n, alpha) be the class of block graphs on n vertices and prescribed independence number alpha. In this article we prove that the maximum spectral radius rho(G), among all graphs G is an element of G(n, alpha), is reached at a unique graph. As a byproduct we obtain an upper for rho(G), when G is an element of G(n, alpha). (C) 2020 Elsevier Inc. All rights reserved.