DISTANCE MAGIC GRAPHS - A SURVEY

S. Arumugam (Kalasalingam University)
Dalibor Froncek (University of Minnesota)
N. Kamatchi (Kalasalingam University)

Journal of the Indonesian Mathematical Society
Special Edition, Year 2011

Let <i>G = (V;E)</i> be a graph of order n. A bijection <i>f : V &rarr; {1, 2,...,n} </i>is called <i>a distance magic labeling </i>of G if there exists a positive integer k such that <i>&Sigma; f(u) = k </i> for all <i>v &epsilon; V</i>, where <i>N(v)</i> is the open neighborhood of v. The constant k is called the magic constant of the labeling f. Any graph which admits <i>a distance magic labeling </i>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