  Let $\mathcal{B}(n,q)$ be the class of block graphs on $n$ vertices having
all their blocks of the same size. We prove that if $G\in \mathcal{B}(n,q)$ has
at 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 bound
for $\rho(G)$ when $G\in \mathcal{B}(n,q)$.
