Note: A note on power domination in grid graphs

Authors:
Michael Dorfling;Michael A. Henning
Affiliations:
School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa;School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 2
Cited 3

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

Journal of Graph Theory
Domination in Graphs Applied to Electric Power Networks

SIAM Journal on Discrete Mathematics

Restricted power domination and fault-tolerant power domination on grids

Discrete Applied Mathematics
On the power domination number of the generalized Petersen graphs

Journal of Combinatorial Optimization
Generalized power domination of graphs

Discrete Applied Mathematics

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Abstract

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graphs (see [T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, M.A. Henning, Power domination in graphs applied to electrical power networks, SIAM J. Discrete Math. 15(4) (2002) 519-529]). A set S of vertices is defined to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. In this paper, we determine the power domination number of an nxm grid graph.