%0 Journal Article
%T The Graceful Labelings of P2r,2m<br>图P2r,2m的优美标号
%A Yan Qiantai
%A <br>严谦泰
%J 系统科学与数学
%D 2006
%I 
%X 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.
%K Graceful graph
%K vertex labeling
%K edge labeling<br>优美图
%K 顶点标号
%K 边标号
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=7B8F991650E8C6A3&yid=37904DC365DD7266&vid=96C778EE049EE47D&iid=94C357A881DFC066&sid=F9A6B6F259CE5121&eid=5A751AE9FA58A3FB&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=3&reference_num=7