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arXiv · 2412.06399

Spectral extremal results on the $A_\alpha$-spectral radius of graphs without $K_{a,b}$-minor

Xingyu Lei·Shuchao Li
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Abstract

An important theorem about the spectral Tur\'an problem of $K_{a,b}$ was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete result is then used to better understand the relationship between the $A_{\alpha}$-spectral radius and the structure of the corresponding extremal $K_{a,b}$-minor free graph.

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Xingyu Lei, Shuchao Li. 2024-12-09. Spectral extremal results on the $A_\alpha$-spectral radius of graphs without $K_{a,b}$-minor. https://doi.org/10.1016/j.amc.2024.129232

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