Further Results On k-Super Graceful 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 graphs in which each component is either regular or bi-regular.

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