Power domination in product graphs - Archive ouverte HAL
Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2008

Power domination in product graphs

Résumé

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 of G is the minimum cardinality of a power dominating set. Dorfling and Henning 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. We also determine the power domination number for the strong product and the lexicographic product of two arbitrary paths.
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Dates et versions

hal-00414504 , version 1 (09-09-2009)

Identifiants

Citer

Paul Dorbec, Sandi Klavzar, Michel Mollard, Simon Spacapan. Power domination in product graphs. SIAM Journal on Discrete Mathematics, 2008, 22 (2), pp.554-567. ⟨10.1137/060661879⟩. ⟨hal-00414504⟩
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