Power domination in maximal planar graphs

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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https://hal.archives-ouvertes.fr/hal-01550353
Contributor : Claire Pennarun <>
Submitted on : Tuesday, December 10, 2019 - 11:20:03 AM
Last modification on : Monday, January 13, 2020 - 1:18:48 AM

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  • HAL Id : hal-01550353, version 3
  • ARXIV : 1706.10047

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

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