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也是优美的.
Let u and ν 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.
基金
国家自然科学基金资助项目(60143002)
关键词
优美图
顶点标号
边标号
graceful graph
vertex labeling
edge labeling.
