On locating-dominating sets in infinite grids

Authors:
Iiro Honkala;Tero Laihonen
Affiliations:
Department of Mathematics, University of Turku, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland
Venue:
European Journal of Combinatorics
Year:
2006

Citing 7
Cited 4

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On identifying codes that are robust against edge changes

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Optimal (r,≤3) -locating-dominating codes in the infinite king grid

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Abstract

Determining a malfunctioning component in a processor network gives the motivation for locating-dominating sets. It is shown that the smallest possible density of a locating-dominating set in the king grid equals 1/5 and in the hexagonal mesh 1/3. Moreover, we discuss a natural modification of locating-dominating sets.