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Please use this identifier to cite or link to this item: http://purl.org/purl/4201

Title: Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes
Authors: Kannan, Balakrishnan
Manoj, Changat
Henry, Martyn Mulder
Ajitha, Subhamathi R
Keywords: Antimedian
consensus function
consensus axiom
Issue Date: 4-Mar-2011
Publisher: World Scientific Publishing Company
Abstract: An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a 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.
Description: Discrete Mathematics, Algorithms and Applications
URI: http://dyuthi.cusat.ac.in/purl/4201
Appears in Collections:Dr. Kannan Balakrishnan

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