| 引用本文: | 戴丽,王正华,谢政.P3，4m的优美性.[J].国防科技大学学报,2005,27(5):126-128.[点击复制] |
| DAI Li,WANG Zhenghua,XIE Zheng.The Gracefulness of P3，4m[J].Journal of National University of Defense Technology,2005,27(5):126-128[点击复制] |
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| P3，4m的优美性 |
| 戴丽1, 王正华2, 谢政1 |
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(1.国防科技大学 理学院，湖南 长沙 410073;2.国防科技大学 计算机学院，湖南 长沙 410073)
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| 摘要: |
| 设u、v是两个固定顶点，用b条内部互不相交且长度均为a的道路连接u、v所得到的图用Pa,b表示。Kathiresan证实P2r,2m-1（r,m均为任意正整数）是优美的，且猜想：除了(a,b)=(2r+1,4s+2)外，所有的Pa,b都是优美的。杨元生已证实P2r+1,2m-1是优美的。本文证明P3，4m是优美图，从而当a=3时Kathiresan猜想成立。 |
| 关键词: 优美图 顶点标号 边标号 |
| DOI： |
| 投稿日期：2005-04-20 |
| 基金项目: |
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| The Gracefulness of P3，4m |
| DAI Li1, WANG Zhenghua2, XIE Zheng1 |
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(1.College of Science,National Univ.of Defense Technology,Changsha 410073,China;2.College of Computer, National Univ. of Defense Technology, Changsha 410073, China)
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| Abstract: |
| Let u and v be two fixed vertices. Connect u and v by b internally disjoint paths of length a , the resulting graphs denoted by Pa,b.Kathiresan showed that P2r,2m-1 is graceful and conjectured that Pa,b is graceful except for (a,b)=(2r+1,4s+2).Yang showed that P2r+1,2m-1 are graceful. In this paper ,P3，4m is proved to be graceful. So we prove the conjecture for a=3. |
| Keywords: graceful graph vertex labeling edge labeling |
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