关于有向图nC^→3的优美性  

On the Gracefulness of Directed Graph nC^→3

作　　者：伊莲娜 关美玲 斯琴其木格 吉日木图[1] Lobsanova Elena;GUAN Mei-ling;Siqinqimuge;Jirimutu(College of Mathematics and Physics,Inner Mongolia University for Nationalities,Tongliao 028043,China;College of Mathematics and Computer Science,Chifeng University,Chifeng 024000,China)

机构地区：[1]内蒙古民族大学数理学院,内蒙古通辽028043 [2]赤峰学院数学与计算机科学学院,内蒙古赤峰024000

出　　处：《内蒙古民族大学学报（自然科学版）》2020年第3期185-190,251,共7页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金项目(912067);内蒙古民族大学研究生科研创新资助项目(NMDSS1730)。

摘　　要：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.

关 键 词：有向图 有向3-回路 优美标号 优美图 

分 类 号：O157.5[理学—数学]