Conditional matroidal edge connectivity of Cayley graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-05-14 DOI:10.1016/j.dam.2025.05.011

Li Wang , Mingxi Su , Liqing Lin , Xiaohui Hua

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引用次数: 0

Abstract

Edge connectivity is an important indicator to evaluate edge fault tolerance. As for a host of networks, the edge connectivity is exactly equal to their minimum degree. Conditional matroidal edge connectivity is a new graph edge connectivity parameter that can be defined when a partition of the edge set is given. It is a good indicator to restrict the different kinds of faulty edges. However, the determination of conditional matroidal edge connectivity is often limited by the edge transitivity of the corresponding graph. In this paper, we use the algebraic technique to conquer the limitation of edge transitivity and give a new method to calculate the conditional matroidal edge connectivity of Cayley graphs. As an application, we not only show the conditional matroidal edge connectivity of varietal hypercube

V Q_{n}

, but also verify the conditional matroidal edge connectivity of alternating group graph

A G_{n}

that was studied by Zhang et al. (2022).

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Cayley图的条件矩阵边连通性

边缘连通性是评估边缘容错能力的重要指标。对于一组网络，其边缘连通性正好等于其最小度。条件矩阵边连通性是一种新的图边连通性参数，它可以在给定边集的划分时定义。这是一个很好的指标来限制不同类型的缺陷边。然而，条件矩阵边连通性的确定往往受到相应图的边传递性的限制。本文利用代数技术克服了边缘可传递性的局限性，给出了一种计算Cayley图条件矩阵边连通性的新方法。作为应用，我们不仅展示了品种超立方体VQn的条件矩阵边连通性，还验证了Zhang等（2022）研究的交替群图AGn的条件矩阵边连通性。

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 Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.