关于有向图nC^→3的优美性

On the Gracefulness of Directed Graph nC^→3

马克杰在《优美图》一书中介绍了几类有向图优美性的研究情况,并提出若干个继续研究的公开问题和猜想,其中猜想"当n为偶数时,有向图nC^→3是优美图"至今还没有被彻底解决.本文用差分模式的方法和完全3-一致超图的理论研究有向图nC^→3的优美性,得到当n≡0(mod2)且2≤n≤16时,有向图nC^→3是优美的.

In his book"Graceful Graph",Make Jie introduces research on the gracefulness of several types of directed graphs,and puts forward a number of open questions and conjectures for further research. Among these is the conjecture"When n is an even number,directed graphs nC^→3 are graceful graphs"which has not been completely solved.We use the method of difference mode and the theory of complete 3-uniform hypergraph to study the Gracefulness of directed graph nC^→3. We obtain that when n ≡ 0(mod2)and 2 ≤ n ≤ 16,directed graph nC^→3 is graceful.