The Bounds of Generalized 4-Connectivity of Folded Divide-and-Swap Cubes

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-08-10 DOI:10.1142/s0219265923500160

Caixi Xue, Shuming Zhou, Hong Zhang

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引用次数: 0

Abstract

Connectivity along with its extensions are important metrices to estimate the fault-tolerance of interconnection networks. The classic connectivity [Formula: see text] of a graph [Formula: see text] is the minimum cardinality of a vertex set [Formula: see text] such that [Formula: see text] is connected or a single vertex. For any subset [Formula: see text] with [Formula: see text], a tree [Formula: see text] in [Formula: see text] is called an [Formula: see text]-tree if [Formula: see text]. Furthermore, any two [Formula: see text]-tree [Formula: see text] and [Formula: see text] are internally disjoint if [Formula: see text] and [Formula: see text]. We denote by [Formula: see text] the maximum number of pairwise internally disjoint [Formula: see text]-trees in [Formula: see text]. For an integer [Formula: see text], the generalized [Formula: see text]-connectivity of a graph [Formula: see text] is defined as [Formula: see text] and [Formula: see text]. For the [Formula: see text]-dimensional folded divide-and-swap cubes, [Formula: see text], we show the upper bound and the lower bound of [Formula: see text], that is [Formula: see text], where [Formula: see text] and [Formula: see text] in this paper.

查看原文本刊更多论文

折叠分换立方体的广义4连通性的界

连通性及其扩展是评估互连网络容错性的重要指标。图的经典连通性[公式:见文]是顶点集[公式:见文]的最小基数，使得[公式:见文]是连通的或单个顶点。对于任何具有[公式:见文本]的子集[公式:见文本]，[公式:见文本]中的树[公式:见文本]称为[公式:见文本]树，如果[公式:见文本]。此外，任意两个[公式:见文]-树[公式:见文]和[公式:见文]在内部是不相交的，如果[公式:见文]和[公式:见文]。我们用[公式:见文]表示[公式:见文]中成对内部不相交的[公式:见文]-树的最大数目。对于整数[公式:见文]，广义[公式:见文]-图[公式:见文]的连通性定义为[公式:见文]和[公式:见文]。对于[公式:见文]维折叠分换立方体，[公式:见文]，我们给出[公式:见文]的上界和下界，即[公式:见文]，其中本文的[公式:见文]和[公式:见文]。

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

JOURNAL OF INTERCONNECTION NETWORKS COMPUTER SCIENCE, THEORY & METHODS-

自引率

14.30%

发文量

121

期刊介绍： The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.