完全对换网络的嵌入连通度

丁秀艳; 艾尔肯·吾买尔

doi:10.13568/j.cnki.651094.2019.01.005

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完全对换网络的嵌入连通度

数理科学 | 更新时间：2026-01-21

- 完全对换网络的嵌入连通度
- 完全对换网络的嵌入连通度
- 新疆大学学报（自然科学版中英文） 2019年36卷第1期页码：34-38
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金项目(11361060,1170149)
- DOI：10.13568/j.cnki.651094.2019.01.005
  中图分类号： O157.5
- 纸质出版：2019
- 稿件说明：
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[1]丁秀艳,艾尔肯·吾买尔.完全对换网络的嵌入连通度[J],2019,36(01):34-38.
[1]丁秀艳,艾尔肯·吾买尔.完全对换网络的嵌入连通度[J],2019,36(01):34-38. DOI： 10.13568/j.cnki.651094.2019.01.005.

DOI：10.13568/j.cnki.651094.2019.01.005.

摘要

一个n维的递归交互网络Gn的一个点(边)子集称为Gn的一个h-嵌入点(边)割(如果这样的子集存在的话)

使得删去这个点(边)子集后得到的图是不连通的且每个点都在一个未损坏的h-维子网络Gh中.图Gn的h-嵌入(边)连通度

记为ζh(Gn)(ηh(Gn))

定义为Gn的最小h-嵌入点(边)割的基数.完全对换网络CTn是网络设计中一类重要的Cayley图.在本文中

我们确定了完全对换网络的h-嵌入(边)连通度:ζh(CTn)=h!/2[n(n-1)-h(h-1)]

其中2≤h≤n-2

ηh(CTn)=h!/2[n(n-1)-h(h-1)]

其中2≤h≤n-1.

Abstract

For an n-dimensional recursive interconnection network Gn

the h-embedded connectivity of Gn

denoted by ζh(Gn)(resp. the h-embedded edge-connectivity of Gn

denoted by ηh(Gn))

is the cardinality of a minimum subset of vertices(resp. edges)

if any

whose deletion disconnects Gn and each vertex of remaining components is contained in an undamaged h-dimensional subnetwork Gh. Complete-transposition graphs CTn are a class of important Cayley graphs in network design. In this paper

we determine ζh andηh for complete-transposition graphs: ζh(CTn) =h!/2[n(n-1)-h(h-1)] for 2 ≤ h ≤ n-2

and ηh(CTn) =h!/2[n(n-1)-h(h-1)] for 2 ≤ h ≤ n-1.

关键词

Keywords

references

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