ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Discussiones Mathematicae Graph Theory 23(2) (2003) 261-272
Bert L. Hartnell
Saint Mary's UniversityHalifax, Nova Scotia, Canada B3H 3C3
Douglas F. Rall
Furman UniversityGreenville, SC 29613, USA
In addition, a number of authors have established bounds for dominating the Cartesian product of any two graphs. We show how it is possible to improve some of these bounds by imposing conditions on both graphs. For
example, we establish a new lower bound for the domination number of T T, when T is a tree, and we improve an upper bound of Vizing in the case when one of the graphs has k > 1 dominating sets which cover the vertex set and the other has a dominating set which partitions in a certain way.
Keywords: domination number, Cartesian product, Vizing's conjecture, 2-packing.
2000 Mathematics Subject Classification: 05C69. ˘
Received 1 October 2001Revised 20 January 2002