满足a(H)=3的图的充分条件

A SUFFICIENT CONDITION FOR THE GRAPHS WITH a (H) = 3

本文给出了满足α(H)=3的图的一个充分条件,从而完整地刻划了文[3]给出的图类的结构特征。设n和m均为自然数.H是任意一个图,其直径d(H)=d_H(x_1,x_2)=2m-1。H=(V(H),E(H)),其中本文证明了如下定理:定理.设n>m,若H的子图H满足A.有;B.使,则α(H)=3。

Suppose that m and n are pasitive integers. Let H be a graph, d(H)=d_H(x_1,x_2)=2m-1. H=(V(H), E(H)). where andA suffient condition for graphs with a(H)=3 is given by the following theorem. Theorem. Let n>m. If subgrph H satisfiesA. For every u∈V(H) d_H(u,x_1)+d_H(u, x_2)≤2m;B. There exist a v_0∈V(H), such that d_H(v_0,x_1)=d_H(v_0, x_2), then a(H)=3.