P_(5,4m)的优美性  

Gracefulness of P_(5,4m)

作　　者：戴丽[1] 王正华[2] 谢政[1] 

机构地区：[1]国防科技大学理学院,长沙410073 [2]国防科技大学计算机学院,长沙410073

出　　处：《数学理论与应用》2008年第1期45-48,共4页Mathematical Theory and Applications

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m=2n(2l-1),(0≤n≤4,l∈N)时,P5,4m是优美图。Let uand v be two fixed vertices. Connecting u and v by b internally disjoint paths of length a, the resulting graphs denoted by Pa,b. KM.Kathiresan showed that P2r,2m-1 is fraceful and conjectured that Pa,b is graceful except when （a,b）=（2r ＋ 1,4s ＋ 2）. YS Yang showed that P2r＋1,2m-1 are graceful, in this paper, P5,4m is proved to be graceful, where m = 2^n（21 - 1）, （0≤n≤4, l∈N）.

关 键 词：优美图 顶点标号 边标号 

分 类 号：O157.5[理学—数学] O158[理学—基础数学]