Odd and even edge magic total labeling

Abstract

An \((m,n)\) graph $G$ is edge magic if there exists a bijective function \(f:V\left( G \right) \cup E\left( G \right) \to \left\{ {1,2,3, \ldots ,m + n} \right\}\) such that \(f\left( u \right) + f\left( v \right) + f\left( {uv} \right) = k\) is a constant, called the valence of $f$, for any edge $uv$ of $G$. Moreover, $G$ is said to be super edge magic if \(f\left( {V\left( G \right)} \right) = \{ 1,2,3, \ldots ,n\} \). In this paper, we introduce odd and even edge magic total labeling.