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 $\mathbf{Bl}(\text{k},\phi )$ be the class of block graphs on $\text{k}$ vertices with given dissociation number $\phi$. In this article, we have shown the existence and uniqueness of a block graph ${\mathbb{B}}_{\text{k},\phi }$ in $\mathbf{Bl}(\text{k},\phi )$ that maximizes the spectral radius $\rho (G)$ among all graphs $G$ in $\mathbf{Bl}(\text{k},\phi )$. Furthermore, we also provide bounds on $\rho ({\mathbb{B}}_{\text{k},\phi })$.