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- W4300688116 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 $ge$ 6 admits a power dominating set of size at most (n--2)/4 ." @default.
- W4300688116 created "2022-10-04" @default.
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- W4300688116 date "2017-06-30" @default.
- W4300688116 modified "2023-10-16" @default.
- W4300688116 title "Power domination in maximal planar graphs" @default.
- W4300688116 doi "https://doi.org/10.48550/arxiv.1706.10047" @default.
- W4300688116 hasPublicationYear "2017" @default.
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