Some Distance Magic Graphs

Let G = (V, E) be a graph of order n. A bijective function f:V→{1,2,…,n} is said to be a distance magic labeling of G if for every v∈V, ∑x∈N(v)f(x)=k (a constant). A graph which admits such a labeling is said to be a distance magic graph. In this paper we study distance magic labeling for the neighborhood expansion Dp(G) of a graph G and present a method for embedding regular graphs into distance magic graphs.