Elegant labeling of some graphs and their line graphs

An elegant labeling f of graph G with ‘ q ’ edges an injective function from the vertices of G to the set {0, 1 , 2,------- q} such that when each edge ( e = xy ) is assigned the label { ( f (x) + f (y) ) mod( q + 1) } the resulting edge labels are distinct and non zero. In this paper it is shown to be certain families of line graphs of elegant graphs are elegant graphs.