A lower bound on the size of k-neighborhood in generalized cubes

被引：8
|
作者：
Yang, Xiaofan [1 ]
Megson, Graham M.
Cao, Jianqiu
Luo, Jun
机构：
[1] Chongqing Jiaotong Univ, Sch Comp & Informat, Chongqing 400074, Peoples R China
[2] Chongqing Univ, Coll Comp Sci, Chongqing 400030, Peoples R China
[3] Univ Reading, Sch Syst Engn, Dept Comp Sci, Reading RG6 6AY, Berks, England
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 179卷 / 01期
基金：
中国国家自然科学基金;
关键词：
interconnection network; hypercube; generalized cube; k-neighborhood;
D O I：
10.1016/j.amc.2005.11.080
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：47 / 54
页数：8
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