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PreprintCC BY 4.0arXiv

Maxima of the Q-index: Forbidden an odd wheel

  • Hongyu Wang
  • Yue Ma
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Abstract

In 2013, Freitas, Nikiforov and Patuzzi (EJLA, 2013) proposed the problem of determining the maximum signless Laplacian spectral radius of an n-vertex F-free graph. Recently, Yuan, Zhai and Zhang (LAA, 2026) determined the maximum signless Laplacian spectral radius of graphs without wheels of sufficiently large order. In this paper, we consider the problem of forbidding a single wheel W2k+1=K1∨ C2k. We show that, for every fixed integer k≥ 3 and sufficiently large n, the unique extremal graph maximizing the signless Laplacian spectral radius among all n-vertex W2k+1-free graphs is Kk∨(K2∪(n−k−2)K1).

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Cite

BibTeXRIS
BibTeX
@misc{wang2026maxima,
  title = {{Maxima of the Q-index: Forbidden an odd wheel}},
  author = {Hongyu Wang and Yue Ma},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00817},
  eprint = {2611.00817},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00817},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Maxima of the Q-index: Forbidden an odd wheel
AU  - Hongyu Wang
AU  - Yue Ma
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00817
UR  - https://arxiv.org/abs/2611.00817
AB  - In 2013, Freitas, Nikiforov and Patuzzi (EJLA, 2013) proposed the problem of determining the maximum signless Laplacian spectral radius of an n-vertex F-free graph. Recently, Yuan, Zhai and Zhang (LAA, 2026) determined the maximum signless Laplacian spectral radius of graphs without wheels of sufficiently large order. In this paper, we consider the problem of forbidding a single wheel W_2k+1=K_1∨ C_2k. We show that, for every fixed integer k≥ 3 and sufficiently large n, the unique extremal graph maximizing the signless Laplacian spectral radius among all n-vertex W_2k+1-free graphs is K_k∨(K_2∪(n−k−2)K_1).
ER  -