On the spectral radius of graphs without a gem

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-17 DOI:10.1016/j.disc.2024.114171

引用次数: 0

Abstract

The gem is the 5-vertex graph consisting of a 4-vertex path plus a vertex adjacent to each vertex of the path. A graph is said to be gem-free if it does not contain gem as a subgraph. In this paper, we consider the spectral extremal problem for gem-free graphs with given size. The maximum spectral radius of gem-free graphs with size $m \geq 11$ is obtained, and the unique corresponding extremal graph is determined.

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关于无宝石图的谱半径

gem 是由 4 个顶点的路径加上与路径上每个顶点相邻的顶点组成的 5 顶点图。如果一个图的子图中不包含 gem，则称该图为无 gem 图。本文考虑的是给定大小的无 gem 图的谱极值问题。我们得到了大小为 m≥11 的无 gem 图形的最大谱半径，并确定了唯一对应的极值图形。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.