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Identifying codes for infinite triangular grids with a finite number of rows

Rennan Dantas 1 Frédéric Havet 2 Rudini Sampaio 1
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Let G be a graph G. The neighborhood of a vertex v in G, denoted by N (v), is the set of vertices adjacent to v i G. It closed neighborhood is the set N [v] = N (v) ∪ {v}. A set C ⊆ V (G) is an identifying code in G if (i) for all v ∈ V (G), N [v] ∩ C = ∅, and (ii) for all u, v ∈ V (G), N [u] ∩ C = N [v] ∩ C. In this paper, we give some bounds on the minimum density of an identifying code in triangular grids of bounded height.
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https://hal.archives-ouvertes.fr/hal-01411109
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Submitted on : Wednesday, December 7, 2016 - 9:27:10 AM
Last modification on : Friday, March 27, 2020 - 4:02:11 PM
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Rennan Dantas, Frédéric Havet, Rudini Sampaio. Identifying codes for infinite triangular grids with a finite number of rows. Bordeaux Graph Workshop 2016, Nov 2016, Bordeaux, France. ⟨hal-01411109⟩

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