一类链图的优美性

对于由k个完全二部图K2,m1,K2,m2,…,K2,mk(其中k,n,m1,m2,…,mk为大于1的正整数)经过不同的粘接方法而得到的链图T1、链图T2、链图T5的优美性进行了研究。在此基础上对由链图T1和长为n的路Pn的一个端点粘接得到的链图T3和链图T2与长为n的路Pn的一个端点粘接得到的链图T4的优美性进行了研究。用构造的方法给出了这几类图的优美标号,得出这些图都是优美图。这样将m1,m2,…,mk的值均为2的范围扩大到大于1的正整数,从而拓宽了优美图及其应用的道路。最后提出了将链图T1、T2、T3、T4、T5分别首尾粘接而得到的一些图是优美图的猜想。

The Gracefulness of A Kind of Chain Graph

The study of the gracefulness of chain graph was undertaken.The chain graph was referred to graph T1、T2、T5,which is linked with k complete two partite graph K2,m1,K2,m2,…,K2,mk(of which k,n,m1,m2,…,mk are all the positive integer greater than 1).The study aimed at the gracefulness of chain graph T3 and T4,T3 is formed by the linkage of chain T1 and path Pn(of which the length is n),T4 is formed by the linkage of chain graph T2 and path Pn(of which the length is n).The graceful labeling was given to these kinds of graphs by construction method,and their graceness were proved.In the above study,the numerical value of m1,m2,…,mk can be expanded from 2 to the positive integer greater than 1,which can widen the road of the graceful graph and its application.At last,a supposition that some graphs respectively linked end to end with chain graph T1、T2、T3、T4、T5 could be graceful was put forward.