Problem detail · source-aware
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Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on $n-2$ vertices is the unique planar graph of maximum adjacency spectral radius for every $n \ge 9$. Tait and Tobin proved it for sufficiently large $n$ in 2017; the conjecture now holds for all $n \ge 9$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The declaration credits the model with generating the code that searched for extremal planar graphs, and with assisting in several computations and symbolic derivations, alongside language polishing.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.