| 非连通图Wmk∪G的优美性 |
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| 引用本文： | 王涛,王清,李德明.非连通图Wmk∪G的优美性[J].合肥工业大学学报(自然科学版),2012(7):987-990. |
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| 作者姓名： | 王涛 王清 李德明 |
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| 作者单位： | 华北科技学院基础部;首都师范大学数学系 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 优美图 优美标号 非连通图 |
Gracefulness of disconnected graphs Wmk∪G |
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| WANG Tao,WANG Qing,LI De-ming.Gracefulness of disconnected graphs Wmk∪G[J].Journal of Hefei University of Technology(Natural Science),2012(7):987-990. |
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| Authors: | WANG Tao WANG Qing LI De-ming |
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| Institution: | 1.Department of Basic Courses,North China Institute of Science and Technology,Sanhe 065201,China;2.Dept.of Mathematics,Capital Normal University,Beijing 100048,China) |
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| Abstract: | 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 connected graph after the hub vertex merging of k wheel Wmi(i=1,2,…,k).When m1 is greater or equal to three,and n is greater or equal to ,the disconnected graphs Wm1(k)∪St(n) are graceful.For any natural number p,which is not less than one,the graph W2p+2+i(k)∪Gpi is graceful,in which the Gpi 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)∪(C3∨■) is graceful. |
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| Keywords: | graceful graph graceful labeling disconnected graph |
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