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Dalibor Froncek
University of Minnesota
Mathematics

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DISTANCE MAGIC GRAPHS - A SURVEY S. Arumugam; Dalibor Froncek; N. Kamatchi
Journal of the Indonesian Mathematical Society Special Edition, Year 2011
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.0.0.15.11-26

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
DECOMPOSITIONS OF COMPLETE GRAPHS INTO KAYAK PADDLES Dalibor Froncek; Leah Tollefson
Journal of the Indonesian Mathematical Society Special Edition, Year 2011
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.0.0.17.39-44

Abstract

A canoe paddle is a cycle attached to an end-vertex of a path. It was shown by Truszczynski that all canoe paddles are graceful and therefore decompose complete graphs. A kayak paddle is a pair of cycles joined by a path. We prove that the complete graph K<sub>2n+1</sub> is decomposable into kayak paddles with <i>n</i> edges whenever at least one of its cycles is eve.DOI : http://dx.doi.org/10.22342/jims.0.0.17.39-44
Co-Authors Leah Tollefson N. Kamatchi S. Arumugam