Graceful Labeling Format

The graceful labeling format is a list of labels whose positions correspond to the vertex they label. For instance, a labeling might be a list (3 0 2 1) which would label a graph which has 4 vertices. $\mathit{Label}(0) \leftarrow 3$, $\mathit{Label}(1) \leftarrow 0$, $\mathit{Label}(1) \leftarrow 2$, etc.