Some Distance Magic Graphs

Abstract 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 D p ( G ) of a graph G and present a method for embedding regular graphs into distance magic graphs.