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Let $\mathcal{B}(n,q)$ be the class of block graphs on $n$ vertices havingall their blocks of the same size. We prove that if $G\in \mathcal{B}(n,q)$ hasat most three pairwise adjacent cut vertices then the minimum spectral radius$\rho(G)$ is attained at a unique graph. In addition, we present a lower boundfor $\rho(G)$ when $G\in \mathcal{B}(n,q)$.

On the spectral radius of block graphs having all their blocks of the same size