Distance magic graphs

Abstract

Let G = (V, E) be a graph of order n. A bijection f : V -> {1, 2, ..., n} is called a distance magic labeling of G if there exists a positive integer k such that Sigma(u is an element of N(v)) f(u) = k for all v is an element of V, where N(v) is the open neighborhood of v. The constant k is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. In this paper we present several results on distance magic graphs along with open problems.