Geodesic
On Vizing's conjecture
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 5-11

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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(G ⃞ H) ≥ 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 
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Bresar, Bostjan. On Vizing's conjecture. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 5-11. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a0/