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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2019

Power domination in maximal planar graphs

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Abstract

Power domination in graphs emerged from the problem of monitoring an electrical system by placing as few measurement devices in the system as possible. It corresponds to a variant of domination that includes the possibility of propagation. For measurement devices placed on a set S of vertices of a graph G, the set of monitored vertices is initially the set S together with all its neighbors. Then iteratively, whenever some monitored vertex v has a single neighbor u not yet monitored, u gets monitored. A set S is said to be a power dominating set of the graph G if all vertices of G eventually are monitored. The power domination number of a graph is the minimum size of a power dominating set. In this paper, we prove that any maximal planar graph of order n ≥ 6 admits a power dominating set of size at most (n−2)/4 .
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Dates and versions

hal-01550353 , version 1 (30-06-2017)
hal-01550353 , version 2 (21-10-2019)
hal-01550353 , version 3 (10-12-2019)

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Paul Dorbec, Antonio González, Claire Pennarun. Power domination in maximal planar graphs. Discrete Mathematics and Theoretical Computer Science, 2019, vol. 21 no. 4, ⟨10.23638/DMTCS-21-4-18⟩. ⟨hal-01550353v3⟩
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