Power domination on triangular grids with triangular and hexagonal shape

Prosenjit Bose (), Valentin Gledel (), Claire Pennarun () and Sander Verdonschot ()
Additional contact information
Prosenjit Bose: Carleton University
Valentin Gledel: Université de Lyon, Université Lyon 1
Claire Pennarun: Univ. Montpellier
Sander Verdonschot: Carleton University

Journal of Combinatorial Optimization, No 0, 19 pages

Abstract: Abstract The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set $$S \subseteq V(G)$$S⊆V(G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M, this neighbor is added to M. The power domination number of a graph G is the minimum size of a set S such that this process ends up with the set M containing every vertex of G. We show that the power domination number of a triangular grid $$H_k$$Hk with hexagonal-shaped border of length $$k-1$$k-1 is $$\left\lceil \dfrac{k}{3} \right\rceil $$k3, and the one of a triangular grid $$T_k$$Tk with triangular-shaped border of length $$k-1$$k-1 is $$\left\lceil \dfrac{k}{4} \right\rceil $$k4.

Keywords: Planar graphs; Regular grid; Power domination (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-020-00587-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00587-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-020-00587-z

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().