非连通图W_m^(k)∪G的优美性  

Gracefulness of disconnected graphs W_m^(k)∪G

作　　者：王涛[1] 王清[1] 李德明[2] 

机构地区：[1]华北科技学院基础部,河北三河065201 [2]首都师范大学数学系,北京100048

出　　处：《合肥工业大学学报（自然科学版）》2012年第7期987-990,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(10201022);北京市自然科学基金资助项目(1102015);中央高校基本科研业务费资助项目(2011B019)

摘　　要：文章证明了对任意自然数n≥1,p≥1,k≥1,当m1=2p+3或2p+4时,图W(k)m1∪Kn,p为优美图,其中Wm1(k)为由k个轮Wmi(i=1,2,…,k)的中心顶点合并后构成的连通图;当m1≥3,n≥[m1/2]时,非连通图Wm1(k)∪St(n)为优美图;对任意自然数p≥1,图W2p+2+i(k)∪Gip为优美图,其中,Gpi表示p条边的i-优美图(i=1,2);对任意自然数n≥1,当m1=2n+5时,图Wm1(k)∪(C3∨■)为优美图。It is proved that for any natural numbers n, p, k, which are not less than one, when m1 =2p＋3 or m1 =2p＋4, the disconnected graphs Wm1（k）∪Kn,p are graceful, in which the Wm1（k） is the cormected graph after the hub vertex merging of k wheel Win, （i=1,2,…,k）. When ml is greater or equal to three, and n is greater or equal to [m1/2], the disconnected graphs Wm1（k）∪St（n） are graceful. For any natural number p, which is not less k） than one, the graph W2p＋2＋i（k）∪Gp is graceful, in which the Gp is the i-graceful graph（i=1,2） with p sides. For any natural number n, which is not less than one, when m1=2n＋5, the graph Wm1（k）∪（C3Vkn） is graeful.

关 键 词：优美图 优美标号 非连通图 

分 类 号：O157.5[理学—数学]