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

Let 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 ∈ B ( n , q ) has at most three pairwise adjacent cut vertices then the minimum spectral radius ρ ( G ) is attained at a unique graph. In addition, we present a lower bound for ρ ( G ) when G ∈ B ( n , q ) .