Power Domination in Product Graphs

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number P (G) of G is the minimum cardinality of a power dominating set. Dorfling and Henning [2] determined the power domination number of the Cartesian product of paths. In this paper the power domination number is determined for all direct products of paths except for the odd component of the direct product of two odd paths. For instance, if n is even and C a connected component of Pm

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Paul Dorbec, Michel Mollard, Sandi Klavzar, Simon Spacapan
• Keywords: Direct Product, Electric Power, Power Domination Number, SIAMDM 2008