Some distance magic graphs

A graph G=(V,E), where |V|=n and |E|=m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set {1,2,…,n} such that, ∑v∈N(u)f(v)=k, for all u∈V, which is a constant and independent of u, where N(u) is the open neighborhood of the vertex u. The constant k is called the distance magic constant of the graph G and such a labeling f is called distance magic labeling of G. In this paper, we present new results on distance magic labeling of Cnr and neighborhood expansion Dn(G) of a graph G.