Distance magic circulant graphs

Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection l : V -> {1, 2,...,n} for which there exists a positive integer k such that Sigma(x is an element of N(nu))l(x) = k for all nu is an element of V, where N(nu) is the neighborhood of nu. In this paper we deal with circulant graphs C-n(1, p). The circulant graph C-n(1, p) is the graph on the vertex set V = {x(0), x(1),...,x(n-1)} with edges (x(i), x(i+p)) for i = 0,...,n-1 where i+p is taken modulo n. We completely characterize distance magic graphs C-n(1,p) for p odd. We also give some sufficient conditions for p even. Moreover, we also consider a group distance magic labeling of C-n(1,p). (C) 2015 Elsevier B.V. All rights reserved.