一致最优完全多部图(英文)

梁晓东; 孟吉翔; 张昭

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一致最优完全多部图(英文)

研究精粹 | 更新时间：2026-01-21

- 一致最优完全多部图(英文)
- 一致最优完全多部图(英文)
- 新疆大学学报（自然科学版中英文） 2012年29卷第1期页码：1-8
- 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：
  
  supported by NSF(2010211A06)of Xinjiang;BS(090106)of Xinjiang University
- DOI：
  中图分类号： O157.5
- 纸质出版：2012
- 稿件说明：
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[1]梁晓东,孟吉翔,张昭.一致最优完全多部图(英文)[J].新疆大学学报(自然科学版),2012,29(01):1-8.

梁晓东, 孟吉翔, 张昭. 一致最优完全多部图(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(1): 1-8.
[1]梁晓东,孟吉翔,张昭.一致最优完全多部图(英文)[J].新疆大学学报(自然科学版),2012,29(01):1-8. DOI：

梁晓东, 孟吉翔, 张昭. 一致最优完全多部图(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(1): 1-8. DOI：

摘要

假设图G的边可靠

而顶点可靠的独立概率为p

以(n

m)表示具有n个顶点m条边的图的集合.若对于所有1 p∈(0

图G均为(n

m)中的最可靠图

则称G为一致最优图.本文证明了完全k部图K(b

(b+1)k h 1

(b+2)h)在其图类中是一致最优的

而当i≥3时

完全k部图K(b

(b+1)k h 2

(b+2)h

b+i)在其图类中不是一致最优的.

Abstract

For a graph G

suppose that edges never fail and vertices operate independently of each other with a constant probability p.Denote by(n

m) the set of graphs with n vertices and m edges.The graph G is called uniformly optimal in(n

m) if

for all vertex-failure probabilities 1 p ∈(0

the graph G is the most reliable graph.This paper proves that the complete k-partite graphs K(b

(b+1) k h 1

(b+2) h) are uniformly optimal in their classes

while for i ≥ 3

the complete k-partite graphs K(b

(b + 1) k h 2

(b + 2) h

b + i) are not uniformly optimal in their classes.

关键词

Keywords

references

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