On 14-regular distance magic graphs

Abstract

Let G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G) -> {1, 2, ... , n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for all vertices v in V(G). A graph which admits a distance magic labeling is a distance magic graph. In this paper, we completely characterize all orders for which a 14 -regular distance magic graph exists. Hereby we extended similar results on 2-, 4-, 6-, 8-, 10-, and 12 -regular distance magic graphs.