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arXiv · 2007.08023

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

Cristian M. Conde·Ezequiel Dratman·Luciano N. Grippo
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Abstract

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 $G\in \mathcal{B}(n,q)$.

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Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo. 2020-07-15. On the spectral radius of block graphs having all their blocks of the same size. https://arxiv.org/abs/2007.08023

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