On k-Super Graceful Labeling of Regular and Bi-regular Graphs

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $p$ and size $q$. For $kge 1$, a bijection $f: V(G)cup E(G) {k, k+1, k+2, ldots, k+p+q-1}$ such that $f(uv)= |f(u) - f(v)|$ for every edge $uvin E(G)$ is said to be a $k$-super graceful labeling of $G$. 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 regular and bi-regular graphs.