The median procedure on median graphs

A median of a profile π = ( x 1, …, x k ) of vertices of a finite connected graph G is a vertex x for which ∑ k i = 1 d( x, x i ) is minimum, where d is the usual geodesic distance on G. The function Med whose domain is the set of all profiles and is given by Med( π) = { x: x is a median of π} is ca...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 84; no. 1; pp. 165 - 181
Main Authors McMorris, F.R., Mulder, Henry Martyn, Roberts, Fred S.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 15.05.1998
Amsterdam Elsevier
New York, NY
Subjects
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Graph theory
Information retrieval. Graph
Mathematics
Sciences and techniques of general use
Theoretical computing
Graph colouring
Connected graph
Vertex(graph)
Graph theory
Finite graph
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Summary:A median of a profile π = ( x 1, …, x k ) of vertices of a finite connected graph G is a vertex x for which ∑ k i = 1 d( x, x i ) is minimum, where d is the usual geodesic distance on G. The function Med whose domain is the set of all profiles and is given by Med( π) = { x: x is a median of π} is called the median procedure on G. In this paper, the median procedure is characterized for median graphs and cube-free median graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(98)00003-1