Brualdi–Hoffman–Turán problem of the gem

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-09 DOI:10.1016/j.disc.2025.114528

Fan Chen , Xiying Yuan

引用次数: 0

Abstract

A graph is said to be F-free if it does not contain F as a subgraph. Brualdi–Hoffman– Turán type problem seeks to determine the maximum spectral radius of an F-free graph with given size. The gem consists of a path on 4 vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi–Hoffman–Turán type problem of the gem, when the size is odd, Zhang and Wang (2024) [20] and Yu et al. (2025) [18] solved it. In this paper, we completely solve the Brualdi–Hoffman–Turán type problem of the gem.

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Brualdi-Hoffman-Turán宝石问题

如果一个图不包含F作为子图，我们就说它是无F的。Brualdi-Hoffman - Turán型问题旨在确定给定尺寸的无f图的最大谱半径。宝石由4个顶点的路径组成，以及与路径的每个顶点相邻的附加顶点。对于宝石的Brualdi-Hoffman-Turán类型问题，当尺寸为奇数时，Zhang and Wang(2024)[20]和Yu et al.(2025)[18]解决了该问题。本文彻底解决了宝石的Brualdi-Hoffman-Turán型问题。

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.