图的λ_4-最优性的邻域交条件  

Neighborhood Intersection Conditions for λ_4-Optimality of a Graph

作　　者：高敬振[1] 黄丽[1] 

机构地区：[1]山东师范大学数学科学学院,山东济南250014

出　　处：《山东科学》2010年第6期5-8,共4页Shandong Science

基　　金：国家自然科学基金项目(10901097)

摘　　要：本文给出了图的λ4-最优性的邻域交条件:设图G是阶数大于等于11的λ4-连通图,对G的任意一对不相邻顶点u,v,若u,v均不在三角形中,有|N(u)∩N(v)|≥5,若u或v在三角形中,有|N(u)∩N(v)|≥7,则G是λ4-最优的;若G中任意一对不相邻顶点u,v满足|N(u)∩N(v)|≥5,任意一条边xy满足|N(x)∩N(y)|≤2,则G也是λ4-最优的.这些结果在网络可靠性分析中有一定应用.This paper presents two neighborhood intersection conditions for λ4-optimality in a graphs.Let G be a λ4-connected graph of order greater than 11.If the inequality ｜N（u）∩N（v）｜≥5 holds and neither u nor v lies on a triangle（u and v are nonadjacent vertices）,or the inequality ｜N（u）∩N（v）｜≥7 holds and either u or v lies on a triangle,then G is λ4-optimal.If the inequality ｜N（u）∩N（v）｜≥5 holds and any one edge xy holds the inequality ｜N（x）∩N（y）｜≤2,then G is also λ4-optimal.These results can be applied to the analysis of network reliability.

关 键 词：图 4-限制边连通度 λ4-最优性 

分 类 号：O157.5[理学—数学]