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Please use this identifier to cite or link to this item: http://purl.org/purl/4237

Title: Median graphs, the remoteness function, periphery transversals, and geodetic number two
Authors: Kannan, Balakrishnan
Bostjan, Brešar
Manoj, Changat
Wilfried, Imrich
Sandi, Klavzar
Matjaz, Kovse
Ajitha, Subhamathi R
Keywords: median graph
median set
remoteness function
geodetic number
periphery transversal
Issue Date: 25-Mar-2008
Abstract: A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed
Description: University of Ljubljana Institute of Mathematics, Physics and Mechanics Department of Mathematics Preprint series, Vol. 46 (2008), 1046
URI: http://dyuthi.cusat.ac.in/purl/4237
ISSN: 1318-4865
Appears in Collections:Dr. Kannan Balakrishnan

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