On the nontrivial extremal eigenvalues of graphs

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics Pub Date : 2025-06-01 Epub Date: 2025-02-11 DOI:10.1016/j.disc.2025.114423

Wenbo Li, Shiping Liu

引用次数: 0

Abstract

We present improved bounds on a quantitative version of an observation originally due to Breuillard, Green, Guralnick and Tao which says that for finite non-bipartite Cayley graphs, once the nontrivial eigenvalues of their normalized adjacency matrices are uniformly bounded away from 1, then they are also uniformly bounded away from −1. Unlike previous works which depend heavily on combinatorial arguments, we rely more on analysis of eigenfunctions. We establish a new explicit lower bound for the gap between −1 and the smallest normalized adjacency eigenvalue, which improves previous lower bounds in terms of edge-expansion, and is comparable to the best known lower bound in terms of vertex-expansion.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

图的非平凡极值特征值

我们在最初由Breuillard， Green， Guralnick和Tao提出的一个观察结果的定量版本上给出改进的界，该观察结果表明，对于有限非二部Cayley图，一旦它们的归一化邻接矩阵的非平凡特征值一致有界远离1，那么它们也一致有界远离- 1。不像以前的工作严重依赖于组合参数，我们更多地依赖于本征函数的分析。我们为−1和最小归一化邻接特征值之间的间隙建立了一个新的显式下界，这在边扩展方面改进了以前的下界，并且在顶点扩展方面与最知名的下界相当。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

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.

期刊最新文献

Leaf to leaf path lengths in trees of given degree sequence Generalized snake posets, order polytopes, and lattice-point enumeration A note on the spectral radius and [a,b]-factor of graphs Construction of Hermitian self-dual constacyclic codes with square-root-like lower bounds on the minimum distances Stoimenow matchings avoiding multiple Catalan patterns simultaneously