λ5-最优图的围长条件  

A Girth Condition for Graphs to be λ5-optimal

作　　者：徐子钧[1] 张磊[1] 赵永耀 XU Zi-jun;ZHANG Lei;ZHAO Yong-yao(School of Mathematics,Jinzhong University,Jinzhong 030619,Shanxi,China)

机构地区：[1]晋中学院数学学院,山西晋中030619

出　　处：《兰州文理学院学报（自然科学版）》2020年第3期1-4,共4页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金资助项目(61370001);晋中学院博士基金资助项目(bsjj2016202)。

摘　　要：设G=(V,E)是连通图,S为G的边割.若G-S的每个分支中至少包含k个点,则称S是G的k限制边割,称所含边数最少的k限制边割的基数为G的k限制边连通度,记为λk(G).定义ξk(G)=min{[X,Y]∶|X|=k,G[X]连通,Y=V(G)\X}.如果λk(G)=ξk(G),那么G是λk-最优的.给出了阶v(G)≥21的λ5-最优图的围长条件.For a connected network G=(V,E),an edge set S E is a k-restricted edge cut if G-S is disconnected and every component of G-S has at least k vertices.The k-restricted edge connectivity of G,denoted byλk(G),is defined as the cardinality of a minimum k-restricted edge cut.Letξk(G)=min{[X,Y]∶|X|=k,G[X],where Y=V(G)\X}.A graph G is maximally k-restricted edge connected ifλk(G)=ξk(G).In this paper,a girth condition is presented for graphs to beλ5-optimal.

关 键 词：λ5-最优图 5限制边连通度 围长 

分 类 号：O157.5[理学—数学]