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Dalibor Froncek
University of Minnesota
Mathematics

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DISTANCE MAGIC GRAPHS - A SURVEY Arumugam, S.; Froncek, Dalibor; Kamatchi, N.
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 iG = (V;E)/i be a graph of order n. A bijection if : V rarr; {1, 2,...,n} /iis called ia distance magic labeling /iof G if there exists a positive integer k such that iSigma; f(u) = k /i for all iv epsilon; V/i, where iN(v)/i is the open neighborhood of v. The constant k is called the magic constant of the labeling f. Any graph which admits ia distance magic labeling /iis 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 Froncek, Dalibor; Tollefson, Leah
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 Ksub2n+1/sub is decomposable into kayak paddles with in/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