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[1]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]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
58卷
期数:
2019年01期
页码:
79-82
栏目:
研究论文
出版日期:
2019-01-24

文章信息/Info

Title:
Sufficient conditions for graphs to be λ’-optimal
文章编号:
0438-0479(2019)01-0079-04
作者:
郭利涛1*郭晓峰2
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):
GUO Litao1*GUO Xiaofeng2
1.School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China; 2.School of Mathematical Sciences,Xiamen University,Xiamen 361005,China
关键词:
限制性边连通度 λ’-最优 逆度
Keywords:
restricted edge connectivity λ’-optimal inverse degree
分类号:
O 157
DOI:
10.6043/j.issn.0438-0479.201707034
文献标志码:
A
摘要:
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.

参考文献/References:

[1] BONDY J A,MURTY U S R.Graph theory and its application[M].New York:Academic Press,1976:1-50.
[2] ESFAHANIAN A H,HAKIMI S L.On computing a conditional edge connectivity of a graph[J].Information Processing Letters,1988,27:195-199.
[3] FAJTLOWICZ S.On conjectures of Graffiti,Ⅲ[J].Congressus Numerantium,1988,66:23-32.
[4] DANKELMANN P,SWART H C,VAN DEN BERG P.Diameter and inverse degree[J].Discrete Math,2008,308:670-673.
[5] DANKELMANN P,HELLWIG A,VOLKMANN L.Inverse degree and edge-connectivity[J].Discrete Math,2009,309:2943-2947.
[6] 郭利涛,徐兰,郭晓峰.极大3-限制性边连通图的若干充分条件[J].厦门大学学报(自然科学版),2011,50(3):498-500.
[7] TIAN Y,GUO L,MENG J,et al.Inverse degree and super edge-connectivity[J].International Journal of Computer Mathematics,2012,89:752-759.

备注/Memo

备注/Memo:
收稿日期:2017-07-22 录用日期:2018-10-04
基金项目:国家自然科学基金(11301440,11771362); 福建省中青年教师教育科研项目(JAT160350); 福建省自然科学基金(2015J05017)
*通信作者:ltguo2012@126.com
更新日期/Last Update: 1900-01-01