Journal
DISCRETE MATHEMATICS
Volume 306, Issue 15, Pages 1812-1816Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.disc.2006.03.037
Keywords
domination; power domination; claw-free; neighbor; private neighbor
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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 domination problem in graphs. In 1998, Haynes et al. considered the graph theoretical representation of this problem as a variation of the domination problem. They defined a set S 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 power domination number gamma(P)(G) of a graph G is the minimum cardinality of a power dominating set of G. In this paper, we present upper bounds on the power domination number for a connected graph with at least three vertices and a connected claw-free cubic graph in terms of their order. The extremal graphs attaining the upper bounds are also characterized. (c) 2006 Published by Elsevier B.V.
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