A function f is a graceful valuation of a graph G with n edges if f is an injection from the vertices of G to the set {dollar}rm{lcub}0,1,...,n{rcub}{dollar} such that, when each edge {dollar}rm{lcub}u, v{rcub}{dollar} is assigned the label {dollar}vert f{dollar} (u) {dollar}-f{dollar} (v){dollar}vert,{dollar} the resulting edge labels are distinct. This labeling provides a sequential labeling of the edges from 1 to n. Any graph that can be gracefully labeled is a graceful graph. If, in addition, there is a number {dollar}gamma{dollar} so that for each edge {dollar}{lcub}{dollar}u, v{dollar}{rcub}{dollar} either f (u) {dollar}legamma展开▼
机译：如果f是从G的顶点到集合{dollar} rm {lcub} 0,1，...，n {rcub} {dollar}的注入，则函数f是具有n个边的图G的优美估计。即，当每个边{dollar} rm {lcub} u时，v {rcub} {dollar}被分配标签{dollar} vert f {dollar}（u）{dollar} -f {dollar}（v）{dollar} vert {dollar}所得到的边缘标签是不同的。该标记提供了从1到n的边缘的连续标记。可以优雅地标记的任何图形都是优美的图形。此外，如果还有一个数字{dollar} gamma {dollar}，这样对于每个边{dollar} {lcub} {dollar} u，v {dollar} {rcub} {dollar}要么是f（u）{dollar} legamma 展开▼
