# Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

 dc.contributor.author Kannan, Balakrishnan dc.contributor.author Manoj, Changat dc.contributor.author Henry, Martyn Mulder dc.contributor.author Ajitha, Subhamathi R dc.date.accessioned 2014-07-22T06:19:16Z dc.date.available 2014-07-22T06:19:16Z dc.date.issued 2011-03-04 dc.identifier.uri http://dyuthi.cusat.ac.in/purl/4201 dc.description Discrete Mathematics, Algorithms and Applications en_US dc.description.abstract An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a en_US vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. 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 such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes. dc.description.sponsorship Cochin University of Science and Technology en_US dc.language.iso en en_US dc.publisher World Scientific Publishing Company en_US dc.subject Antimedian en_US dc.subject consensus function en_US dc.subject consistency en_US dc.subject path en_US dc.subject hypercube en_US dc.subject consensus axiom en_US dc.title Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes en_US dc.type Article en_US
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