k-strong gracefulness of graphs F_m~((t))
Deming Li · Journal of Hefei University of Technology · 2013
The k-strong gracefulness of graphs Fm(t) is studied.By using the definition of k-strong graceful graph,it is showed that for any natural number t,which is not less than one,when k=,the graphs Fm(t) are k-strong graceful,and the disconnected graphs Fm(t) ∪Gk-1 are graceful.If m is greater or equal to 2p+2,the disconnected graphs Fm(t) ∪Kn,p are graceful,where Fm is a fan with m+1 vertices,Fm(t) is a connected graph by identifying the central vertices of Fm,F2m,…,F2t-1m,and Gk-1 is a graceful graph with k-1 edges.