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

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

**Authors : **

Sindhu Murugan ^{1*} and S. Chandra Kumar ^{2}

**Author Address : **

^{1} Research Scholar, Reg No-18213162092011, Scott Christian College(Autonomous), Nagercoil-629003, Tamil Nadu, India.

Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012, Tamil Nadu, India.

^{2} Department of Mathematics, Scott Christian College(Autonomous), Nagercoil-629003, Tamil Nadu, India.

*Corresponding author.

**Abstract : **

An $H$-magic labeling in an $H$-decomposable graph $G$ is a bijection $f : V (G)cup E(G) ightarrow {1, 2, ldots, p+q}$ such that for every copy $H$ in the decomposition, $sumlimits_{v in V(H)} f(v) + sumlimits_{e in E(H)}f(e)$ 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.

**Keywords : **

$H$-decomposable graph, $H$-factorable graph, $H$-magic labeling, $H$-$V$-super magic labeling, 2-factor-$V$-super magic.

**DOI : **

**Article Info : **

*Received : * November 21, 2018; *Accepted : * March 09, 2019.