Gracefulness of disconnected graphs W_m~(k)∪G
Deming Li · Journal of Hefei University of Technology · 2012
It is proved that for any natural numbers n,p,k,which are not less than one,when m1=2p+3 or m1=2p+4,the disconnected graphs Wm1(k)∪Kn,p are graceful,in which the Wm1(k) is the connected graph after the hub vertex merging of k wheel Wmi(i=1,2,…,k).When m1 is greater or equal to three,and n is greater or equal to ,the disconnected graphs Wm1(k)∪St(n) are graceful.For any natural number p,which is not less than one,the graph W2p+2+i(k)∪Gpi is graceful,in which the Gpi is the i-graceful graph(i=1,2) with p sides.For any natural number n,which is not less than one,when m1=2n+5,the graph Wm1(k)∪(C3∨■) is graceful.