H-V- super magic labeling of H-factorable graphs

Abstract

An $H$-magic labeling in an $H$-decomposable graph $G$ is a bijection $f: V(G) \cup E(G) \rightarrow\{1,2, \ldots, p+q\}$ such that for every copy $H$ in the decomposition, $\sum_{v \in V(H)} f(v)+\sum_{e \in E(H)} f(e)$ is constant. The function $f$ is said to be $H$ - $V$-super magic labeling if $f(V(G))=\{1,2, \ldots, p\}$. In this article, we give a few fundamental properties of $H$ - $V$-super magic labeling. Obtained the magic constant for $H$-factorable graphs which are $H$-V-super magic. Further we gave a necessary and sufficient condition for an even regular graph to be 2 -factor- $V$-super magic.