Fault-free Hamiltonian cycles in faulty arrangement graphs

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题名:	Fault-free Hamiltonian cycles in faulty arrangement graphs
作者:	Hsieh,SY;Chen,GH;Ho,CW
贡献者:	資訊工程研究所
关键词:	HYPERCUBES;NETWORKS;DEBRUIJN;MESHES;RINGS;TREES
日期:	1999
上传时间:	2010-06-29 20:14:55 (UTC+8)
出版者:	中央大學
摘要:	The arrangement graph A(n,k), which is a generalization bf the star graph (n - k = 1), presents more flexibility than the star graph in adjusting the major design parameters: number of nodes, degree, and diameter. Previously, the arrangement graph has proved Hamiltonian. In this paper, we further show that the arrangement graph remains Hamiltonian even ii it is faulty. Let \F-e\ and \F-v\ denote the numbers of edge faults and vertex faults, respectively. We show that A(n,k) is Hamiltonian when 1) (k = 2 and n - k greater than or equal to 4, or k greater than or equal to 3 and n - k greater than or equal to 4 + inverted right perpendicular k/2 inverted left perpendicular), and \F-e\ less than or equal to k(n - k) - 2, or 2) k greater than or equal to 2, n - k greater than or equal to 2 + inverted right perpendicular k/2 inverted left perpendicular, and \F-e\ less than or equal to k(n - k - 3) - 1, or 3) k greater than or equal to 2, n - k greater than or equal to 3, and \F-e\ less than or equal to k, or 4) n - k greater than or equal to 3 and \F-v\ less than or equal to n - 3, or 5) n - k greater than or equal to 3 and \F-v\ + \F-e\ less than or equal to k. Besides, for A(n,k) with n - k = 2, we construct a cycle of length at least 1) n!/(n-k)! - 2 if \F-e\ less than or equal to k - 1, or 2) n!/(n-k)! - \F-v\ - 2(k -1) if \F-v\ less than or equal to k - 1, or 3) n!/(n-k)! - \F-v\ - 2(k - 1) if \F-e\ + \F-v\ less than or equal to k - 1, where nl/(n-k)l is the number of nodes in A(n,k).
關聯:	IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
显示于类别:	[資訊工程研究所] 期刊論文

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