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Axiomatic Characterization of the Median and Antimedian Functions on Cocktail-Party Graphs and Complete Graphs

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  • Changat, M.
  • Lekha, D.S.
  • Mulder, H.M.
  • Subhamathi, A.R.

Abstract

__Abstract__ A median (antimedian) of a profile of vertices on a graph $G$ is a vertex that minimizes (maximizes) the remoteness value, that is, the sum of the distances to the elements in the profile. The median (or antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (or obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper an axiomatic characterization is obtained for the median and antimedian functions on complete graphs minus a perfect matching (also known as cocktail-party graphs). In addition a characterization of the antimedian function on complete graphs is presented.

Suggested Citation

  • Changat, M. & Lekha, D.S. & Mulder, H.M. & Subhamathi, A.R., 2014. "Axiomatic Characterization of the Median and Antimedian Functions on Cocktail-Party Graphs and Complete Graphs," Econometric Institute Research Papers EI 2014-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:77639
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    References listed on IDEAS

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    1. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    2. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    3. McMorris, F.R. & Mulder, H.M. & Ortega, O., 2010. "Axiomatic Characterization of the Mean Function on Trees," Econometric Institute Research Papers EI 2010-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
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