Total domination number of grid graphs

Authors:
Sylvain Gravier
Affiliations:
CNRS, Laboratoire Leibniz-IMAG, 46 avenue Félix Viallet, 38031 Grenoble Cedex 1, France
Venue:
Discrete Applied Mathematics
Year:
2002

Citing 4
Cited 3

The domination numbers of the 5 x n and 6 x n grid graphs

Journal of Graph Theory
Dominating Cartesian products of cycles

Discrete Applied Mathematics
Algebraic approach to fasciagraphs and rotagraphs

Discrete Applied Mathematics
On domination numbers of Cartesian product of paths

Discrete Applied Mathematics

Total restrained domination in graphs

Computers & Mathematics with Applications
The total bondage number of grid graphs

Discrete Applied Mathematics
Total and paired domination numbers of toroidal meshes

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.04

Visualization

Abstract

We use the link between the existence of tilings in Manhattan metric with {1}-bowls and minimum total dominating sets of Cartesian products of paths and cycles. From the existence of such a tiling, we deduce the asymptotical values of the total domination numbers of these graphs and we deduce the total domination numbers of some Cartesian products of cycles. Finally, we investigate the problem of total domination numbers for some Cartesian products of two paths.