【摘要】 <正> 引言文[1]中,D.Frank Hsu引入了强协调标号(strongly harmonious labelings)的定义:设G是一个n边图,如果存在一个映射φ:V(G)→{0,1,…,n}满足i)φ是单射; ii)Auv∈E(G),令φ(uv)=φ(u)+φ(u),有{φ(uv)|uv∈E(G)}={1,2,…,n},则称G为强协调的,φ为它的一个强协调标号,简称为强协调值。显然,φ导出了一个E(G)与{1,2,…,n)的一一对应。本文的目的,一是求出全体n条边的图的所有强协调值的个数;二是指出几类非强协更多还原

【Abstract】 In paper (1), D. Frank Hsu proposed the notion of strongly harmoniouslabelings of graphs. There are three purposes in this paper:1. Compute the numbers of all strongly harmonious labelings of graphs with n edges. Obtain the followi result: [(n/2)!]~2 n even ((n+1)/2)!((n-1)/2)! n odd2. Show several sorts of graphs which have no strongly, harmonious labelings, for examples: all trees but stars, all bipartite graphs but stars and K_n(n≥ 5), etc. And we have proved that there are only two stroagly harmonious graphs in 3-regular graphs.3, Construct larger strongly harmonious graphs from a given one.更多还原