ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 27(2) (2007) 313-321
DOI: 10.7151/dmgt.1363


Sandi Klavžar

Department of Mathematics and Computer Science
FNM, University of Maribor
Gosposvetska 84, 2000 Maribor, Slovenia

Matjaz Kovse

Institute of Mathematics, Physics and Mechanics
Gosposvetska 84, 2000 Maribor, Slovenia


The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K1 by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.

Keywords: intersection graph, partial cube, median graph, expansion theorem, Cartesian product of graphs.

2000 Mathematics Subject Classification: 05C75, 05C12.


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Received 25 April 2006
Revised 28 December 2006
Accepted 28 December 2006