On super edge-magic total labeling of forests consisting of stars and subdivided stars

Muhammad Imran, Ambreen Mukhtar

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.


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