DISTANCE MAGIC GRAPHS - A SURVEY

S. Arumugam, Dalibor Froncek, N. Kamatchi


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


Keywords


Distance magic labeling, magic constant, fair incomplete tournament

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p-ISSN:2086-8952e-ISSN:2460-0245