Power domination in maximal planar graphs

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 g...

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Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 21 no. 4; no. Graph Theory; pp. COV1 - 24
Main Authors: Dorbec, Paul, González, Antonio, Pennarun, Claire
Format: Journal Article
Language:English
Published: Nancy DMTCS 13.12.2019
Discrete Mathematics & Theoretical Computer Science
Subjects:
[info.info-dm]computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds]computer science [cs]/data structures and algorithms [cs.ds]
Apexes
Computer Science
Data Structures and Algorithms
Discrete Mathematics
Graph theory
Graphs
Mathematical research
maximal planar graph
Measuring instruments
Neighborhoods
power domination
Power electronics
propagation
Set theory
France
power domination
maximal planar graph
propagation
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary: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 .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.23638/DMTCS-21-4-18