On $k$-Super Graceful Labeling of Graphs

Abstract

Let G = (V (G), E(G)) be a simple, finite and undirected graph of order p and size q.We say G is k-super graceful if it admits a k-super graceful labeling. In this paper, we study the k-super gracefulness of some standard graphs. Some general properties are obtained. Particularly, we found many sufficient conditions on k-super gracefulness for many families of (complete) bipartite and tripartite graphs. We show that some of the conditions are also necessary.