Distance magic labeling on shadow graphs

Abstract

Assume that G=G(V, E) is a graph. Let f be a bijection from V to {1, 2,…, v} and w(x)=Σy∊N(x) f(y)=k where ND(x)={y ∊ V/d (x, y) ∊ D} , x ∊ V then such a labeling is called as D-distance magic labeling and a graph G is said to be D-distance magic graph. In the paper, we obtain D-distance magic labeling of shadow graphs of paths, cycles, wheels, star graph and splitting graph. We also obtain a necessary and sufficient condition for the shadow graph Dm(K1,n) to admit (0, 2) - distance magic labeling.