完全图的 k-优美性与优美数

The k-Gracefulness and The Graceful Number of Complete Graph

在k-优美图、k-GL 矩阵(k 为非负整数)的基础上,提出优美数和子段的概念,用子段计算的方法,证得K_n(n≥5)非优美图,又证得K_n(n≥6)非1-优美图.并推出K_n的k-优美标号的性质及某些优美数.

A simple graph G(V,E) is k-graceful(integer k≥0)if there isa labelling (?) of its vertices with distinct integers from the set{0,1,2,…,|E|+k},so that the induced edge labelling L defined by L(uv)=|(?)(u)-(?)(v)|assigns each edge a different labe.In this paper,we give the concepts of the graceful number and the subsec-tion,by means of which we can prove that“K_n(n≥5)are nongraceful”,“K_n(n≥6)are not 1-graceful”.And then we get that the graceful number of K_6(K_5)is two(one),and so on.