# 郭利涛*,郭晓峰.λ’-最优图的充分条件[J].厦门大学学报(自然科学版),2019,58(01):79-82.[doi:10.6043/j.issn.0438-0479.201707034] 　GUO Litao*,GUO Xiaofeng.Sufficient conditions for graphs to be λ’-optimal[J].Journal of Xiamen University(Natural Science),2019,58(01):79-82.[doi:10.6043/j.issn.0438-0479.201707034] 点击复制 λ’-最优图的充分条件(PDF/HTML) 分享到： var jiathis_config = { data_track_clickback: true };

58卷

2019年01期

79-82

2019-01-24

## 文章信息/Info

Title:
Sufficient conditions for graphs to be λ’-optimal

0438-0479(2019)01-0079-04

1.厦门理工学院应用数学学院,福建 厦门 361024; 2.厦门大学数学科学学院,福建 厦门 361005
Author(s):
1.School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China; 2.School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

Keywords:

O 157
DOI:
10.6043/j.issn.0438-0479.201707034

A

G=(V,E)是一个连通图.边集SE,如果G-S不连通且G-S的每个连通分支至少有2个点,则称S是一个限制性边割.限制性边连通度λ’(G)就是G的最小限制性边割的基数.如果限制性边割存在,则称Gλ’-连通的.如果λ’(G)=ξ(G),Gλ’-最优或者极大限制性边连通的,其中ξ(G)=min{|[X,Y]|:XV,|X|=2,G[X]连通}.图G的逆度是指R(G)=∑v∈V1/(d(v)).在此基础上,主要得到了:如果Gλ’-连通围长大于等于5的n阶图,且δ(G)≥2,如果R(G)小于某个关于最小度和顶点数的值,则Gλ’-最优的.对于不含钻石的图也得到了类似的结果.
Abstract:
Let G=(V,E) be a connected graph.An edge set SE is a restricted edge cut,ifG -S is disconnected and every component of G -S contains at least two vertices.The restricted edge connectivity λ’(G) of G is the cardinality of a minimum restricted edge cut of G.A graph G is λ’-connected,if restricted edge cuts exist.A graph G is called λ’-optimal,if λ’=ξ(G),where ξ(G)=min{|[x,y]|:XY,|X|=2,G[X] is connected}.The inverse degree of graphs is R(G)=∑v∈V1/(d(v)).In this paper,we obtain the main result below:let G be a λ’-connected graph,girth g≥5 and δ(G)≥2,if R(G) is smaller than some value about n and δ(G),then,G is λ’-optimal.We also obtain similar results for graphs which do not contain the diamond.

## 备注/Memo

*通信作者:ltguo2012@126.com