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

2026/07/21 by Lele Liu, Bo Ning, Yi Wang
#math.CO

paper · pdf

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.

Citations

• A Conjecture on the Maximum Value of the Principal Eigenvalue of a Planar Graph
• The largest eigenvalue of a graph: A survey

Related

• Three conjectures in extremal spectral graph theory
• On the maximum spectral radius of planar graphs
• The spectral even cycle problem
• Nonregular graphs with a given maximum degree attaining maximum spectral radius
• Extremal problems on planar graphs without k edge-disjoint cycles