Smooth Graceful Graphs And Its Application To Construct Graceful Graphs
V. J. Kaneria, M M Jariya · 2014
In this paper we define smooth graceful labeling and we prove that cycle n C , complete bipartite graph n K 2, and path n P are smooth graceful graphs. Using this smooth graceful labeling we prove that a graph obtained by joining + m C ( 2 ≡ m (mod 4 )) and n C ( 0 ≡ n (mod 4 )) with a path of arbitrary length is graceful. We also prove a graph obtained by joining m C ( 0 ≡ m (mod 4 )) and n W with a path of arbitrary length is graceful.