λ5-最优图的邻域交条件

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λ 5-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(u) ∩N(v) ｜ ≤3 for all edges xy of G, then G is λ5- optimal.