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

Manoj Changat, Divya Lekha, Martyn Mulder and Ajitha Subhamathi

No EI 2014-31, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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.

Keywords: median; antimedian; consensus function; consistency; cocktail-party graph; complete graph; consensus axiom (search for similar items in EconPapers)
Pages: 13
Date: 2014-11-24
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://repub.eur.nl/pub/77639/EI2014-31-volledig.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:77639

Access Statistics for this paper

More papers in Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute Contact information at EDIRC.
Bibliographic data for series maintained by RePub ( this e-mail address is bad, please contact ).