摘要
一个含e条边的简单图G被称为是一个强协调图,若存在V(G)到{0,1,…,e-1}的一个单射h,使导出映射h~*:h~*(uv)=h(u)+h(v)是E(G)到{1,2,…,e}的一个双射。本文证明了图S_m+K_n与S_m+K_2都是强协调图。从而回答了[3]中的一个open问题。
A simple graph G with e edges is said a strong harmonious graph if, there exists an injection h: V(G)→{0, 1,..., e-1}, so that the induced function h~*:h~*(uv)=h(u)+h(v) is a bijection from E(G) to {1, 2, ..., e}. In this paper, it's proved that the graphs S_m+(?)_n S_m+K_2 are strong harmonious graphs, thus an open problem in [3] is answered.
