| 图P2r,2m的优美标号 |
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| 引用本文： | 严谦泰.图P2r,2m的优美标号[J].系统科学与数学,2006,26(5):513-517. |
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| 作者姓名： | 严谦泰 |
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| 作者单位： | 安阳师范学院数学系,安阳,455000 |
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| 基金项目： | 河南省自然科学基金(0511013800)资助． |
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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皆为a的道路连接u,v所得图用P_(a,b)表示．K．M．Kathiresan证明：P_(2r,2m-1)(r,m皆为任意正整数)是优美的,且猜想,除了(a,b)=(2r 1,4s 2)外,所有的P_(a,b)都是优美的．杨元生已证明P_(2r 1,2m-1)是优美的,并且证明了,当r=1,2,3,4,5,6,7时,P_(2r,2m)也是优美的．作者证明：r为任意奇数时,P_(2r,2m)也是优美的．
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| 关 键 词： | 优美图 顶点标号 边标号 |
| 修稿时间： | 2004年11月26 |
The Graceful Labelings of P2r,2m |
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| Yan Qiantai.The Graceful Labelings of P2r,2m[J].Journal of Systems Science and Mathematical Sciences,2006,26(5):513-517. |
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| Authors: | Yan Qiantai |
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| Institution: | Department of Mathematics, Anyang Teachers College, Anyang 45500 |
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| Abstract: | Let $u$ and $v$ be two fixed vertices. Connect $u$ and $v$ by $b$ internally disjoint paths of length $a$ and denote the resulting graphs by $P_{a, b}$.K. M. Kathiresan shows that $P_{2r, 2m-1}$ is graceful and conjectures that $P_{a, b}$ is graceful except when $(a,b)=(2r+1,4s+2)$. Y. S. Yang shows that $P_{2r+1,2m-1}$ and $P_{2r, 2m}(r=1, 2, \cdots, 7)$ are graceful. In this paper, $P_{2r, 2m}$ is proved to be graceful when $r$ is an odd number. |
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| Keywords: | Graceful graph vertex labeling edge labeling |
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