On the spectral radius of clique trees with a given zero forcing number

Abstract

Let $G(n,k)$ be the class of clique trees on $n$ vertices and zero forcing number $k$, where $\left \lfloor \frac{n}{2} \right \rfloor + 1 \le k \le n-1$ and each block is a clique of size at least $3$. In this article, we proved the existence and uniqueness of a clique tree in $G(n,k)$ that attains maximal spectral radius among all graphs in $G(n,k)$. We also provide an upper bound for the spectral radius of the extremal graph.