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PreprintCC BY 4.0arXiv

A complete solution to the Boots-Royle/Cao-Vince conjecture

  • Lele Liu
  • Bo Ning
  • Yi Wang
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Abstract

Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge and a path on n−2 vertices is the unique planar graph of maximum adjacency spectral radius for n≥ 9. Tait and Tobin (JCTB, 2017) proved the conjecture for sufficiently large order. In this paper, we completely resolved the Boots-Royle/Cao-Vince conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026complete,
  title = {{A complete solution to the Boots-Royle/Cao-Vince conjecture}},
  author = {Lele Liu and Bo Ning and Yi Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.19268},
  eprint = {2607.19268},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.19268},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A complete solution to the Boots-Royle/Cao-Vince conjecture
AU  - Lele Liu
AU  - Bo Ning
AU  - Yi Wang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2607.19268
UR  - https://arxiv.org/abs/2607.19268
AB  - Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge and a path on n−2 vertices is the unique planar graph of maximum adjacency spectral radius for n≥ 9. Tait and Tobin (JCTB, 2017) proved the conjecture for sufficiently large order. In this paper, we completely resolved the Boots-Royle/Cao-Vince conjecture.
ER  -