λ_5-最优图的邻域交条件  

Neighborhood Intersection Conditions for λ_5-Optimal Graphs

作　　者：张国珍[1] 王世英[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2011年第2期176-179,共4页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(61070229)

摘　　要：给出了λ5-最优图的邻域交条件:设G是一个阶至少为10的连通图,对G中任意一对不相邻顶点u和v,若u,v均不在三角形中,有|N(u)∩N(v)|≥6,若u或v在三角形中,有|N(u)∩N(v)|≥9,则G是λ5-最优的;若G中任意一对不相邻顶点u和v满足|N(u)∩N(v)|≥7,任意一条边xy满足|N(x)∩N(y)|≤3,则G是λ5-最优的.Neighborhood intersection conditions for λ5-optimal graphs are introduced.Let G be a connected graph with order at least 10.If ｜N（u）∩N（v）｜≥6 for all pairs u,v of nonadjacent vertices of G such that neither u nor v lies on a triangle,and ｜N（u）∩N（v）｜≥9 for all pairs u,v of nonadjacent vertices of G such that either u or v lies on a triangle,then G is λ5-optimal.If ｜N（u）∩N（v）｜≥7 for all pairs u,v of nonadjacent vertices of G,and ｜N（x）∩N（y）｜≤3 for all edges xy of G,then G is λ5-optimal.

关 键 词：限制边割 限制边连通度 邻域 

分 类 号：O157.5[理学—数学]