Connected graphs minimizing the spectral radius for given order and dissociation number

Zejun Huang; Jiahui Liu; Chenxi Yang

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arXiv · 2603.14791

Connected graphs minimizing the spectral radius for given order and dissociation number

Zejun Huang·Jiahui Liu·Chenxi Yang

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Abstract

A dissociation set in a graph is a subset of vertices which induces a subgraph with maximum degree at most one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we consider the $n$-vertex connected graphs with a given dissociation number that attain the minimum spectral radius. By using structure analysis and constructing difference equations, we characterize the extremal graphs with dissociation number $n-3$.

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Zejun Huang, Jiahui Liu, Chenxi Yang. 2026-03-18. Connected graphs minimizing the spectral radius for given order and dissociation number. https://arxiv.org/abs/2603.14791

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