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Infinite Order Domination in Graphs |
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Abstract
The previously studied notions of smart and foolproof finite order domination of a simple graph G = (V,E) are generalised in the sense that safe configurations in G are not merely sought after k >= 1 moves, but in the limiting cases where k tends to infinity. Some general properties of these generalised domination parameters are established, after which the parameter values are found for certain simple graph structures (such as paths, cycles, multipartite graphs and products of complete graphs, cycles and paths).
An electronic version of the complete paper may be obtained here: [ps] [pdf].
Affiliations
1Department of Mathematics and Statistics, University of Victoria, Box 3045, Victoria, BC, Canada,
V8W 3P4, email: alewynburger@hotmail.com.
2 Department of Mathematics and Statistics, University of Victoria, Box 3045, Victoria, BC, Canada,
V8W 3P4, email: e_cockayne@hotmail.com.
3 Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa,
email: wgrundlingh@dip.sun.ac.za.
4 Department of Mathematics and Statistics, University of Victoria, Box 3045, Victoria, BC, Canada,
V8W 3P4, email: mynhardt@math.uvic.ca.
5 Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa,
email: wynand@dip.sun.ac.za.
6 Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa,
email: vuuren@sun.ac.za.