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P2r,6图的优美性
引用本文:容青,熊冬春.P2r,6图的优美性[J].系统科学与数学,2010,30(5):703-709.
作者姓名:容青  熊冬春
作者单位:广西师范学院计算机与信息工程学院,南宁,530023
基金项目:广西教育厅科研项目,广西师范学院青年科研基金 
摘    要:Kathiresan KM证实$P_{2r,2m-1}$($r,m$皆为任意正整数)是优美的且猜想:除了$(a,b)=(2r-1,4m-2)$外,所有的$P_{a,b}$都是优美的.杨元生证实$P_{2r+1,2m+1}$是优美的,并且证实了当$r\leq7$, $r=9$时的$P_{2r,2m}$是优美的.严谦泰证实$r$为奇数时$P_{2r,2m}$是优美的.采用回溯和分支限界算法搜索到了一个适合于所有$P_{2r,b}$图($r,b$皆为任意正整数)的优美标号,用函数构造法提取其规律并从数学的严格性进行了证明,使得所有的$P_{2r,b}$图($r,b$ 皆为任意正整数)的优美性得到了证实.

关 键 词:优美图  顶点标号  边标号.
收稿时间:2009-4-3
修稿时间:2010-1-21

THE GRACEFULNESS OF GRAPH P2r,b
RONG Qing,XIONG Dongchun.THE GRACEFULNESS OF GRAPH P2r,b[J].Journal of Systems Science and Mathematical Sciences,2010,30(5):703-709.
Authors:RONG Qing  XIONG Dongchun
Institution:College of Computer and Information Engineering, Guangxi Teachers Education University, Nanning 530023
Abstract:Kathiresan K M showed that $P_{2r,2m-1}$ is graceful and conjectured that $P_{a,b}$ is graceful except when $a=2r-1$ and $b=4m-2$. Professor Yang Yuansheng showed that $P_{2r+1,2m+1}$ and $P_{2r,2m}$ ($r\leq 7,r=9$) are graceful. Yan Qiantai pointed out that $P_{2r,2m}$ are graceful when $r$ is odd. In this paper, a graceful label adapting to all the $P_{2r,b}$ is searched by trace and branch bound method. So the gracefulness of $P_{2r,b}$ for any positive integers $r$ and $b$ is proved.
Keywords:Graceful graph  vertex labeling  edge labeling  
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