纸质出版日期:2011,
网络出版日期:2011-11-25
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证明了对任意自然数n≥1,p≥1,当m=2p+3,2p+4时,非连通图Wm∪Kn,p和Wm,2m+1∪Kn,p是优美图;当i=1,2时,图W2p+2+i∪G(i)p是优美图。当m≥3,n≥s时,Wm,2m+1∪St(n)是优美图;当m=2n+5时,图Wm,2m+1∪(C3∨Kn)是优美图。
For any natural numbers n,p, which are not less than one, when m=2p+3 or 2p+4, the disconnected graphs Wm∪Kn,pand Wm,2m+1∪Kn,p are graceful; when i=1 or 2, the graph W2p+2+i∪G(i)p is graceful. Ifmis greater than or equal to three, and n is greater than or equal to s, where s is a natural number, Wm,2m+1∪St(n) is graceful; in particular, if m=2n+5, Wm,2m+1∪(C3∨Kn) is graceful.
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