图形中的韧性和谱半径

IF 0.7 3区 数学 Q2 MATHEMATICS
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引用次数: 0

摘要

非完整图 G 的韧性 t(G) 定义为 t(G)=min{|S|c(G-S)} ,其中最小值取自 G-S 断开的所有适当集合 S⊂G,其中 c(G-S) 表示 G-S 的分量数。由 Brouwer 猜想并由 Gu 证明的韧性定理指出,每个 d 规则连通图总是有 t(G)>dλ-1,其中 λ 是邻接矩阵的第二大绝对特征值。1988 年,榎本提出了图 G 的韧性变化 τ(G),其定义为:τ(G)=min{|S|c(G-S)-1,S⊂V(G)和c(G-S)>1}。通过结合韧度的变化和谱条件,我们分别提供了τ-韧(τ≥2 为整数)和τ-韧(1τ 为正整数)且度数δ最小的图的谱条件。此外,我们还研究了平衡双方形图的类似问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Toughness and spectral radius in graphs

The toughness t(G) of a non-complete graph G is defined as t(G)=min{|S|c(GS)} in which the minimum is taken over all proper sets SG such that GS is disconnected, where c(GS) denotes the number of components of GS. Conjectured by Brouwer and proved by Gu, a toughness theorem state that every d-regular connected graph always has t(G)>dλ1, where λ is the second largest absolute eigenvalue of the adjacency matrix. In 1988, Enomoto introduced a variation of toughness τ(G) of a graph G, which is defined by τ(G)=min{|S|c(GS)1,SV(G)andc(GS)>1}. By incorporating the variation of toughness and spectral conditions, we provide spectral conditions for a graph to be τ-tough (τ2 is an integer) and to be τ-tough (1τ is a positive integer) with minimum degree δ, respectively. Additionally, we also investigate a analogous problem concerning balanced bipartite graphs.

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来源期刊
Discrete Mathematics
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.
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