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 $q$. For $k\ge 1$, a bijection $f:V(G)\cup E(G)\to \{k,k+1,k+2,\dots ,k+p+q-1\}$ such that $f(uv)=|f(u)-f(v)|$ for every edge $uv\in E(G)$ 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 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.

arXiv commentWe have eventually split this manuscript into two independent papers for submission. We decided to withdraw this paper to avoid high percentage of similarity check

Cited by in corpus (1)

• Further Results On k-Super Graceful Graphs