图P_(2r，2m)的优美标号  

THE GRACEFUL LABELINGS OF P_(2r,2m)

作　　者：严谦泰[1] 

机构地区：[1]安阳师范学院数学系,安阳455000

出　　处：《系统科学与数学》2006年第5期513-517,共5页Journal of Systems Science and Mathematical Sciences

基　　金：河南省自然科学基金(0511013800)资助.

摘　　要：设u,v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,v所得图用P_(a,b)表示．K．M．Kathiresan证明：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+1,4s+2)外,所有的P_(a,b)都是优美的．杨元生已证明P_(2r+1,2m-1)是优美的,并且证明了,当r=1,2,3,4,5,6,7时,P_(2r,2m)也是优美的．作者证明：r为任意奇数时,P_(2r,2m)也是优美的．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 Pa,b. K. M. Kathiresan shows that P2r,2m-1 is graceful and conjectures that Pa,b is graceful except when （a, b） = （2r ＋ 1, 4s ＋ 2）. Y. S. Yang shows that P2r＋1,2m-i and P2r,2m（r = 1, 2,..., 7） are graceful. In this paper, P2r,2m is proved to be graceful when r is an odd number.

关 键 词：优美图 顶点标号 边标号 

分 类 号：O157.5[理学—数学]