THE GRACEFULNESS OF GRAPH P(2r,b)
Rong Qing, Xiong Dongchun · Xitong kexue yu shuxue · 2010
Kathiresan K M showed that P_(2r,2m-1)is 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+1)and P_(2r,2m)(r≤7,r=9)are graceful.Yan Qiantai pointed out that P_(2r,2m)are graceful when r is odd.In this paper,a graceful label adapting to all the P_(2r,b)is searched by trace and branch bound method.So the gracefulness of P_(2r,b)for any positive integers r and b is proved.