On the spectral Turán problem of theta graphs

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-05-23 DOI:10.1016/j.laa.2024.05.015

Yi Xu, Xin Li

引用次数: 0

Abstract

In 2010, Nikiforov conjectured that for $ℓ \geq 2$ and n sufficiently large, $S_{n, ℓ - 1}^{1}$ is the unique graph with the maximum spectral radius over all n-vertex $C_{2 ℓ}$ -free graphs. In 2022, Cioabǎ, Desai and Tait solved this conjecture. The theta graph $Θ_{t, ℓ}$ consists of two vertices joined by t vertex-disjoint paths, each of length ℓ. Particularly, $Θ_{2, ℓ} ≅ C_{2 ℓ}$ . In this paper, we characterize the unique extremal graph which attains the maximum spectral radius among all $Θ_{t, ℓ}$ -free graphs of order n, where $t, ℓ \geq 3$ and n is sufficiently large.

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论三角形图的图兰谱问题

2010 年，尼基福罗夫猜想，对于 ℓ≥2 和 n 足够大的情况，Sn,ℓ-11 是所有 n 顶点无 C2ℓ 图形中具有最大谱半径的唯一图形。2022 年，Cioabǎ、Desai 和 Tait 解决了这一猜想。θ图 Θt,ℓ由两个顶点通过 tx 个顶点相交的路径连接而成，每个路径的长度为 ℓ。特别是，Θ2,ℓ≅C2ℓ。在本文中，我们描述了在 t,ℓ≥3 且 n 足够大的情况下，所有无 Θt,ℓ 的 n 阶图中达到最大谱半径的唯一极值图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.