eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2019-12-13
vol. 21 no. 4
Graph Theory
10.23638/DMTCS-21-4-18
5127
journal article
Power domination in maximal planar graphs
Paul Dorbec
Antonio González
Claire Pennarun
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 .
https://dmtcs.episciences.org/5127/pdf
propagation
power domination
maximal planar graph
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]