An assignment of integer numbers to the vertices of a given graph under certain conditions is referred to as a graph labeling. The assignment of labels from the set {0,1,2,...,2 1} q to the vertices of G (with ( ) G n V vertices and ( ) q E G edges) such that, when each edge has assigned a label defined by the absolute difference of its end-points, the resulting edge labels are 1,3 ,2 1 q is re...