The g-extra connectivity of graph products

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2024-05-29 DOI:10.1016/j.jcss.2024.103552

Zhao Wang , Yaping Mao , Sun-Yuan Hsieh , Ralf Klasing , Yuzhi Xiao

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引用次数: 0

Abstract

Connectivity is one of important parameters for the fault tolerant of an interconnection network. In 1996, Fàbrega and Fiol proposed the concept of g-extra connectivity. A subset of vertices S is said to be a cutset if $G - S$ is not connected. A cutset S is called an $R_{g}$ -cutset, where g is a non-negative integer, if every component of $G - S$ has at least $g + 1$ vertices. If G has at least one $R_{g}$ -cutset, the g-extra connectivity of G, denoted by $κ_{g} (G)$ , is then defined as the minimum cardinality over all $R_{g}$ -cutsets of G. In this paper, we first obtain the exact value of g-extra connectivity for the lexicographic product of two general graphs. Next, the upper and lower sharp bounds of g-extra connectivity for the Cartesian product of two general graphs are given. In the end, we apply our results on grid graphs and 2-dimensional generalized hypercubes.

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图积的 g 外连接性

连接性是互联网络容错的重要参数之一。1996 年，Fàbrega 和 Fiol 提出了 "额外连通性 "的概念。如果一个顶点子集不连通，则称其为一个。如果切割集的每个分量都至少有顶点，则称为切割集，其中为非负整数。如果至少有一个-切集，那么，表示为，定义为所有-切集的最小心数。在本文中，我们首先获得了两个一般图的词典乘积的-外部连通性的精确值。接着，我们给出了两个一般图的笛卡尔积的-外连通性的上下限。最后，我们将结果应用于网格图和二维广义超立方体。

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 Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.