English

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

Combinatorics 2023-09-28 v1

Abstract

A dissociation set of a graph is a set of vertices which induces a subgraph with maximum degree less than or equal to one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we study the connected graphs of order nn with a given dissociation number that attains the minimum spectral radius. We characterize these graphs when the dissociation number is in {n1, n2, 2n/3, 2n/3, 2}\{n-1,~n-2,~\lceil2n/3\rceil,~\lfloor2n/3\rfloor,~2\}. We also prove that these graphs are trees when the dissociation number is larger than 2n/3\lceil {2n}/{3}\rceil.

Keywords

Cite

@article{arxiv.2309.15597,
  title  = {Connected graphs with a given dissociation number attaining the minimum spectral radius},
  author = {Zejun Huang and Jiahui Liu and Xinwei Zhang},
  journal= {arXiv preprint arXiv:2309.15597},
  year   = {2023}
}
R2 v1 2026-06-28T12:33:39.884Z