ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

DOI 10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2017: 0.601

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 21(1) (2001) 5-11
DOI: 10.7151/dmgt.1129


Bostjan Bresar

University of Maribor, FK, Vrbanska 30
2000 Maribor, Slovenia



A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)−D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G H Vizing's conjecture [10] states that γ(GH) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.

Keywords: graph, Cartesian product, domination number.

2000 Mathematics Subject Classification: 05C69, 05C12.


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Received 9 December 1999
Revised 22 January 2001