ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2018-2019): c. 84%
Mathematicae Graph Theory 21(1) (2001) 5-11DOI: 10.7151/dmgt.1129
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  states that γ(GH)
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.
Received 9 December 1999
Revised 22 January 2001