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PreprintCC BY 4.0arXiv

Minimizing the spectral radius of unicyclic graphs with fixed order and dissociation number

  • Yu Zhou
  • Yuanyuan Chen
  • Dan Li
  • Dandan Fan
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Abstract

A dissociation set of a graph G is a vertex subset S contained in V(G) such that the induced subgraph G[S] has maximum degree at most 1, and the dissociation number of G is the cardinality of a maximum dissociation set denoted by Φ(G). In this paper, we first derive a sharp lower bound on the dissociation number for all unicyclic graphs. Furthermore, we also study the graphs with minimum spectral radius among all unicyclic graphs with given order and dissociation number and explicitly identify all extremal graphs for n−4 ≤ Φ(G) ≤ n−1.

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Cite

BibTeXRIS
BibTeX
@misc{zhou2026minimizing,
  title = {{Minimizing the spectral radius of unicyclic graphs with fixed order and dissociation number}},
  author = {Yu Zhou and Yuanyuan Chen and Dan Li and Dandan Fan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38539},
  eprint = {2610.38539},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38539},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Minimizing the spectral radius of unicyclic graphs with fixed order and dissociation number
AU  - Yu Zhou
AU  - Yuanyuan Chen
AU  - Dan Li
AU  - Dandan Fan
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38539
UR  - https://arxiv.org/abs/2610.38539
AB  - A dissociation set of a graph G is a vertex subset S contained in V(G) such that the induced subgraph G[S] has maximum degree at most 1, and the dissociation number of G is the cardinality of a maximum dissociation set denoted by Φ(G). In this paper, we first derive a sharp lower bound on the dissociation number for all unicyclic graphs. Furthermore, we also study the graphs with minimum spectral radius among all unicyclic graphs with given order and dissociation number and explicitly identify all extremal graphs for n−4 ≤ Φ(G) ≤ n−1.
ER  -