On (Super) Edge-Magic Total Labeling of Subdivision of K1,3

Abstract

Let $G$ be a finite graph, with $V(G)$ and $E(G)$ the vertex-set and edge-set of $G$, respectively. An edge-magic total labeling is a one-to-one mapping $f$ from $V(G)\cup E(G)$ onto $\{1,2,3,\cdots ,|V(G)|+|E(G)\left|\right\}$ such that there exists a constant $c$ satisfying $f(u)+f(uv)+f(v)=c$, for each $uv\in E(G)$. Such a labeling is called a super edge-magic total labeling if all vertices of $G$ receive all smallest labels. In this paper, we consider (super) edge-magic total labeling for subdivision of a star $K_{1,3}$.