Power domination and zero forcing

Abstract

The power domination number arises from the monitoring of electrical networks and its determination is an important problem. Upper bounds for power domination numbers can be obtained by constructions. Lower bounds for the power domination number of several families of graphs are known, but they usually arise from specific properties of each family and the methods do not generalize. In this paper we exploit the relationship between power domination and zero forcing to obtain the first general lower bound for the power domination number. We apply this bound to obtain results for both the power domination of tensor products and the zero-forcing number of lexicographic products of graphs. We also establish results for the zero forcing number of tensor products and Cartesian products of graphs.

References in corpus (1)

• Power propagation time and lower bounds for power domination number

Cited by in corpus (7)

• Characterizations of the Connected Forcing Number of a Graph
• Minimum rank and zero forcing number for butterfly networks
• Graphs with Extremal Connected Forcing Numbers
• The relationship between $k$-forcing and $k$-power domination
• Grundy dominating sequences and zero forcing sets
• Optimal Sensor Placement in Power Grids: Power Domination, Set Covering, and the Neighborhoods of Zero Forcing Forts
• Edge Forcing in Butterfly Networks