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A positive integer $k$ is called a magic constant if there is a graph $G$along with a bijective function $f$ from $V(G)$ to first $|V(G)|$ naturalnumbers such that the weight of the vertex $w(v) = \sum_{uv \in E}f(v) =k$ forall $v \in V$. It is known that all odd positive integers greater equal $3$ andthe integer powers of $2$, $2^{t}$, $t \ge 6$ are magic constants. In thispaper we characterise all positive integers which are magic constants.

A Complete Characterization of all Magic Constants Arising from Distance Magic Graphs