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《Journal of Xiamen University(Natural Science)》 2019-01
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Sufficient conditions for graphs to be λ′-optimal

GUO Litao;GUO Xiaofeng;School of Applied Mathematics,Xiamen University of Technology;School of Mathematical Sciences,Xiamen University;  
Let G=(V,E)be a connected graph.An edge set SEis a restricted edge cut,if G-Sis disconnected and every component of G-S contains at least two vertices.The restricted edge connectivityλ′(G)of Gis the cardinality of a minimum restricted edge cut of G.A graph Gisλ′-connected,if restricted edge cuts exist.A graph Gis calledλ′-optimal,ifλ′=ξ(G),whereξ(G)= min{|[x,y]|:X Y,|X|=2,G[X]is connected}.The inverse degree of graphs is R(G)=∑_v∈V 1/d(v).In this paper,we obtain the main result below:let Gbe aλ′-connected graph,girth g≥5 andδ(G)≥2,if R(G)is smaller than some value about n and δ(G),then,Gisλ′-optimal.We also obtain similar results for graphs which do not contain the diamond.
【Fund】: 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)
【CateGory Index】: O157.5
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1 GUO Li-tao1,XU Lan2,GUO Xiao-feng1(1.School of Mathematical Sciences,Xiamen University,Xiamen 361005,China; 2.Department of Mathematics,Changji College,Changji 831102,China);Sufficient Conditions for Graphs to Be Maximally 3-restricted Edge Connected[J];厦门大学学报(自然科学版);2011-03
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