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arXiv · 2607.04324

Connected graphs with a large dissociation number attaining the minimum spectral radius

Zejun Huang·Chenxi Yang
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Abstract

A dissociation set in a graph is a subset of vertices that induces a subgraph of maximum degree at most one, which is a natural generalization of the notion of an independent set. The dissociation number of a graph is defined as the maximum cardinality of a dissociation set. This paper studies the minimum spectral radius of connected graphs with a given order $n$ and a given dissociation number $\psi$. For $\psi=n-k$ with $k\ge 4$ fixed and $n$ sufficiently large, we establish both upper and lower bounds for this minimum spectral radius and prove the extremal graphs must belong to a specific graph class.

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Zejun Huang, Chenxi Yang. 2026-07-05. Connected graphs with a large dissociation number attaining the minimum spectral radius. https://arxiv.org/abs/2607.04324

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