用禁止子图最大化给定大小的图的谱半径

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-08-05 DOI:10.1016/j.laa.2025.07.032

Yanting Zhang , Ligong Wang

引用次数: 0

摘要

设H7为7顶点扇形图，该扇形图由一条6顶点路径加上与该路径每个顶点相邻的一个顶点组成。设K3∨m−33K1为三角形K3的每个顶点与m−33个孤立顶点相连接得到的图。本文证明了如果G是大小为m≥33的无h7图，则谱半径ρ(G)≤1+m−2，当且仅当G≠K3∨m−33K1（可能有孤立顶点）成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Maximizing the spectral radius of graphs of given size with a forbidden subgraph

Let

H_{7}

denote the 7-vertex fan graph consisting of a 6-vertex path plus a vertex adjacent to each vertex of the path. Let

K_{3} \lor \frac{m - 3}{3} K_{1}

be the graph obtained by joining each vertex of a triangle

K_{3}

\frac{m - 3}{3}

isolated vertices. In this paper, we show that if G is an

H_{7}

-free graph with size

m \geq 33

, then the spectral radius

ρ (G) \leq 1 + \sqrt{m - 2}

, equality holds if and only if

G ≅ K_{3} \lor \frac{m - 3}{3} K_{1}

(possibly, with some isolated vertices).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.