| 杨元生,容青,徐喜荣.一类优美图[J].数学研究及应用,2004,24(3):520~524 |
| 一类优美图 |
| A Class of Graceful Graphs |
| 投稿时间：2001-11-02 |
| DOI：10.3770/j.issn:1000-341X.2004.03.021 |
| 中文关键词: 优美图 顶点标号 边标号 |
| 英文关键词:graceful graph vertex labeling edge labeling. |
| 基金项目:国家自然科学基金资助项目(60143002) |
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| 中文摘要: |
| 设u、ν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、ν所得的图用Pa,b表示.KM.Kathiresan证实P2,2m-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Pa,b都是优美的.杨元生已证实P2r+1,2m-1是优美的,并且证实了当r=1,2,3,4时的P2r,2m也是优美的.本文证实r=5,6,7时P2r,2m
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| 英文摘要: |
| Let u and u be two fixed vertices. Connecting u and v by b internally disjoint paths of length a, the resulting graphs is denoted by Pa,b. KM. Kathiresan showed that P2r,2m-1 is graceful and conjectured that Pa,b is graceful except when (a,b) = (2r+1, 4s + 2). Y. S. Yang showed that P2r+1,2m-1 and P2r,2m (r= 1, 2, 3, 4) are graceful. In this paper, P2r,2m is proved to be graceful for r=5,6,7. |
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