关于图是[a,b;m]-均匀图的一个邻域条件(英文)

A Neighborhood Condition for Graphs to Be [a,b;m]-uniform Graph

设G是一个n阶的图,并设a和b是整数,使得1≤a<b,以及δ(G)是G的最小度.证明了:如果δ(G)≥a+1,n≥2(a+b)(a+b-1)/b,以及|NG(x)∪NG(y)|≥an/(a+b-1)+2对G的任意两个不相邻的顶点x和y都成立,那么G是一个[a,b;m] 均匀图.

Let G be a n-order graph,and let a and b be integers such that 1≤a<b,and δ(G) be the minimum degree. Then it is proved that if δ(G)≥a+1,n≥2(a+b)(a+b-1)/b,and ｜N_G(x)∪(N_G(y)｜≥)an/(a+b-1)+2 for any two non-adjacent vertices x and y of G, then G is an [a,b;m]-uniform graph.