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arXiv · 2301.12790

Maximization of the spectral radius of block graphs with a given dissociation number

Joyentanuj Das·Sumit Mohanty
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Abstract

A connected graph is called a block graph if each of its blocks is a complete graph. Let $\mathbf{Bl}(\textbf{k}, φ)$ be the class of block graphs on $\textbf{k}$ vertices with given dissociation number $φ$. In this article, we have shown the existence and uniqueness of a block graph $\mathbb{B}_{\textbf{k},φ}$ in $\mathbf{Bl}(\textbf{k}, φ)$ that maximizes the spectral radius $ρ(G)$ among all graphs $G$ in $\mathbf{Bl}(\textbf{k}, φ)$. Furthermore, we also provide bounds on $ρ(\mathbb{B}_{\textbf{k},φ})$.

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Joyentanuj Das, Sumit Mohanty. 2023-09-28. Maximization of the spectral radius of block graphs with a given dissociation number. https://arxiv.org/abs/2301.12790

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