【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≤7,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.更多还原

【Abstract】 Kathiresan K M showed that P_2r,2m-1is 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+1and P_2r,2m（r≤7,r=9）are graceful.Yan Qiantai pointed out that P_2r,2mare graceful when r is odd.In this paper,a graceful label adapting to all the P_2r,bis searched by trace and branch bound method.So the gracefulness of P_2r,bfor any positive integers r and b is proved.更多还原