Hamiltonian cycles of balanced hypercube with disjoint faulty edges

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Information Processing Letters Pub Date : 2024-06-20 DOI:10.1016/j.ipl.2024.106518

Ting Lan, Huazhong Lü

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引用次数: 0

Abstract

The balanced hypercube $B H_{n}$ , a variant of the hypercube, is a novel interconnection network topology for massive parallel systems. It is showed in [Theor. Comput. Sci. 947 (2023) 113708] that for any edge subset F of $B H_{n}$ there exists a fault-free Hamiltonian cycle in $B H_{n} - F$ for $n \geq 2$ with $| F | \leq 5 n - 7$ if the degree of every vertex in $B H_{n} - F$ is at least two and there exist no $f_{4}$ -cycles in $B H_{n} - F$ . In this paper, we consider the existence of Hamiltonian cycles of $B H_{n}$ when F is a matching (a set of disjoint edges), and show that each edge $e \notin F$ lies on a fault-free Hamiltonian cycle of $B H_{n} - F$ with $n \geq 2$ . The number of faulty edges in F can be up to $2^{2 n - 1}$ , which is exponential to the dimension n.

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平衡超立方体的哈密顿循环与不相连的故障边

平衡超立方体 BHn 是超立方体的一种变体，是一种用于大规模并行系统的新型互连网络拓扑结构。Theor. Comput. Sci. 947 (2023) 113708]一文指出，对于 BHn 的任意边子集 F，如果 BHn-F 中每个顶点的度至少为 2，且 BHn-F 中不存在 f4-循环，则对于 n≥2 的 BHn-F 中存在一个无故障哈密顿循环，且 |F|≤5n-7 。在本文中，我们考虑了当 F 是一个匹配（一组不相交的边）时 BHn 的哈密顿循环的存在性，并证明了每条边 e∉F 都位于 BHn-F 中 n≥2 的无错哈密顿循环上。F 中故障边的数量可达 22n-1，与维数 n 成指数关系。

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

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.

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