Graphs of Degree at Least [math] with Minimum Algebraic Connectivity

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-09-16 DOI:10.1137/23m1585659

Maryam Abdi, Ebrahim Ghorbani

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2447-2467, September 2024.
Abstract. In 1996 Guiduli and Mohar proposed a conjecture that predicts the structure of connected graphs with minimum degree [math] and minimum algebraic connectivity. We settle this conjecture for the case [math]. As a result, we conclude that the minimum algebraic connectivity of connected graphs with [math] vertices and [math] is [math], where [math] is a function in [math] that tends to 0 as [math] goes to infinity. This enables us to provide a positive answer to the problem of whether graphs with [math] and nearly maximum diameter have asymptotically minimum algebraic connectivity.

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具有最小代数连接性的阶数至少为 [math] 的图形

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2447-2467 页，2024 年 9 月。摘要1996 年，Guiduli 和 Mohar 提出了一个猜想，预测了具有最小度[math]和最小代数连通性的连通图的结构。我们解决了[math]情况下的这一猜想。因此，我们得出结论：具有 [math] 个顶点和 [math] 的连通图的最小代数连通性为 [math]，其中 [math] 是 [math] 中的一个函数，当 [math] 变为无穷大时，它趋向于 0。这使我们能够对具有 [math] 且直径接近最大的图是否具有渐近最小代数连通性的问题给出肯定的答案。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.