Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius
Statement
Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on vertices is the unique planar graph of maximum adjacency spectral radius for every . Tait and Tobin proved it for sufficiently large in 2017; the conjecture now holds for all .
Context
A conjecture posed independently by two groups around 1991 and a standard reference point in spectral extremal graph theory, with Tait and Tobin's asymptotic solution in JCTB.
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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.
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