有向图n·■_m的优美性

On the Gracefulness of the Digraphs n·■_m

给定有向图D(V,E),如果存在一个单射f:V(D)→{0,1,…,|E|}使得对于每条有向边(u,v),诱导函数f′:E(D)→{1,2,…,|E|}是一个双射函数,其中,f′(u,v)=[f(v)-f(u)](mod(|E|+1)),则f称为有向图D(V,E)的优美标号,f′称为有向图D(V,E)的诱导的边的优美标号.本文讨论了有向图n.■m的优美性,并且证明了当m=23且n为偶数时,n.■m是优美有向图.

A digraph D（V,E） is said to be graceful if there exists an injectionf：V（G）→{0,1,…,｜E｜ } such that the induced function f^1 ：E（G） →{1,2,…, ｜E｜} which is defined hy f^1 （u,v） [f（v） -- f（u）]（mod（ ｜E｜ ＋ 1）） for every directed edge （u,v） is a bijection. Here, fis called a graceful labeling （graceful numbering） of D（V,E）, and f^1 is called the induced edge＇s graceful labeling of D. In this paper we discuss the gracefulness of the digraph n· ^→ Cm,and prove that n· ^→ Cm,is a graceful digraph for m=23 and even n.