5等周边连通图的邻域条件

Neighborhood Conditions for 5-isoperimetric Edge Connected Graphs

文章研究了5等周边连通图的领域条件,若G是一个阶至少为10的连通图,对于G中任意一对不相邻的顶点u,v,当u和v都不在三角形中时满足|N(u)∩N(v)|≥4;当u和v中至少有一个在三角形中时满足|N(u)∩N(v)|≥9,则G是γ_5-最优的.

In this paper,a neighborhood condition for graphs to be γ5-optimal is given. Let G be a connected graph with v（ G） at least 10,for any pair u,v of nonadjacent vertices in G,if ｜N（ u）∩N（v） ｜ ≥ 4 when neither u nor v lies on a triangle,or ｜N（u）∩N（ v）｜ ≥ 9 when u or v lies on a triangle,then G is γ5-optimal.