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

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