DISTANCE MAGIC GRAPHS - A SURVEY

S. Arumugam (1) , Dalibor Froncek (2) , N. Kamatchi (3)
(1) Kalasalingam University, India,
(2) University of Minnesota, United States,
(3) Kalasalingam University

Abstract

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

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Authors

S. Arumugam
author@jims-a.org (Primary Contact)
Dalibor Froncek
N. Kamatchi
Author Biographies

S. Arumugam, Kalasalingam University

National Centre for Advanced Researchin Discrete Mathematics (n-CARDMATH)

Dalibor Froncek, University of Minnesota

Department of Mathematics and Statistics,

N. Kamatchi, Kalasalingam University

National Centre for Advanced Researchin Discrete Mathematics (n-CARDMATH)
Arumugam, S., Froncek, D., & Kamatchi, N. (2012). DISTANCE MAGIC GRAPHS - A SURVEY. Journal of the Indonesian Mathematical Society, 11–26. https://doi.org/10.22342/jims.0.0.15.11-26
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