DISTANCE MAGIC GRAPHS - A SURVEY

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 Σ f(u) = k for all v ε 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 a survey of existing results on distance magic graphs along with our recent results,open problems and conjectures.DOI : http://dx.doi.org/10.22342/jims.0.0.15.11-26