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

Lele Liu; Bo Ning; Yi Wang

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

Combinatorics 2026-07-21 v1

Authors: Lele Liu , Bo Ning , Yi Wang

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 $n\geq 9$ . Tait and Tobin (JCTB, 2017) proved the conjecture for sufficiently large order. In this paper, we completely resolved the Boots-Royle/Cao-Vince conjecture.

Cite

@article{arxiv.2607.19268,
  title  = {A complete solution to the Boots-Royle/Cao-Vince conjecture},
  author = {Lele Liu and Bo Ning and Yi Wang},
  journal= {arXiv preprint arXiv:2607.19268},
  year   = {2026}
}

Comments

19 pages, 2 figures