无 3K3 图形的 Q 指数最大值

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-08-21 DOI:10.1016/j.dam.2024.08.004

Yanting Zhang, Ligong Wang

引用次数: 0

摘要

图 G 的 Q 指数是其 Q 矩阵 Q(G)=D(G)+A(G) 的最大特征值，其中 D(G) 和 A(G) 分别是顶点度对角矩阵和 G 的邻接矩阵。让 3K3 表示由三个顶点相交的三角形组成的图。如果一个图的子图中不包含 3K3，则该图被称为无 3K3。本文提出了阶数 n≥453 的无 3K3 图的 Q 指数的尖锐上限，并描述了达到该上限的唯一极值图的特征。

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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Maxima of the Q-index for 3K3-free graphs

The $Q$ -index of a graph $G$ is the largest eigenvalue of its $Q$ -matrix $Q (G) = D (G) + A (G)$ , where $D (G)$ and $A (G)$ are the diagonal matrix of vertex degrees and the adjacency matrix of $G$ , respectively. Let $3 K_{3}$ denote the graph consisting of three vertex-disjoint triangles. A graph is called $3 K_{3}$ -free if it does not contain $3 K_{3}$ as a subgraph. In this paper, we present a sharp upper bound on the $Q$ -index of $3 K_{3}$ -free graphs of order $n \geq 453$ , and characterize the unique extremal graph which attains the bound.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.