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

Cristian M. Conde; Ezequiel Dratman; Luciano N. Grippo

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

Spectral Theory 2020-10-15 v2 Combinatorics

Authors: Cristian M. Conde , Ezequiel Dratman , Luciano N. Grippo

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

Keywords

block graphs spectral radius cut vertices graph blocks lower bound

Cite

@article{arxiv.2007.08023,
  title  = {On the spectral radius of block graphs having all their blocks of the same size},
  author = {Cristian M. Conde and Ezequiel Dratman and Luciano N. Grippo},
  journal= {arXiv preprint arXiv:2007.08023},
  year   = {2020}
}

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