证明了,对任意大于1的自然数m,n,p,非连通图(^—K2V^—Km)∪kn,p是优美图;当k≤P,m=kn+3或m=kn+1时,非连通图(P2V^—Km)∪Kn,p是优美图;当P≥2,m=3k+1时,非连通图(P2V—Km)∪K3,p是优美图;对任意正整数n,P,非连通图(P1VP2n+2)∪Kn,p是优美图.
In this paper, we showed that for natural numbers m, n, p, which are greater than one, the graph(^—K2 V —Km) ∪Kn,p is graceful; when k is equal to or less thanp, and m = kn + 3 or m = kn + 1, the graph (P2 V ^—Km) ∪ Kn,p is graceful; when p is not less than two, and m = 3k + l, (P2 V ^—Km) ∪ Ka,piS graceful; when,n,pare positive integer, (P1 V P2n+2) ∪ Kn,p is graceful.