On Super Edge-Magic Total Labeling of Forests Consisting of Stars and Subdivided Stars

Abstract

A super edge-magic total labeling of a graph $G$ of order $p$ and size $q$ is a~bijection $\lambda:V(G)\cup E(G)\rightarrow \{1, 2, \dots , p+q\}$, where the vertices are labeled with the numbers $1, 2,\dots, p$ and there exists a constant $t$ such that $f(x)+f(xy)+f(y)=t$, for every edge $xy\in E(G)$. In this paper, we study the existence of super edge-magic total labeling of forests with two components consisting of stars and subdivided stars. These results add further support to the conjecture proposed by Figueroa-Centeno \emph {et al.} in 2005.