ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 25(1-2) (2005) 183-196
DOI: 10.7151/dmgt.1271


Bostjan Bresar

University of Maribor, FEECS
Smetanova 17, 2000 Maribor, Slovenia

Pranava K. Jha

Department of Computer Science
St. Cloud State University
720 Fourth Ave. S., St. Cloud, MN 56301, USA

Sandi Klavžar

Department of Mathematics and Computer Science, PEF
University of Maribor
Koroska 160, 2000 Maribor, Slovenia

Blaz Zmazek

University of Maribor, FME
Smetanova 17, 2000 Maribor, Slovenia


Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P3 is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K2 are proved, and it is shown that the only nonbipartite quasi-median direct product is K3×K3.

Keywords: median graph, direct product, quasi-median graph, isometric embeddings, convexity.

2000 Mathematics Subject Classification: 05C75, 05C12.


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Received 29 November 2003
Revised 1 September 2004