Geodesic
Optimal error-detecting open-locating-dominating set on the infinite triangular grid
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 445-455

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Let G be a graph and S ⊆ V(G) represent a subset of vertices having installed “detectors, quot; each of which is capable of sensing an “intruder quot; in its open-neighborhood. The open-locating-code of v ∈ V(G) is the set of neighboring detectors, N(v) ∩ S. The set S is said to be an open-locating-dominating set if every open-locating-code is unique and non-empty. In this paper we focus on error-detecting open-locating-dominating sets on the infinite triangular grid, present a solution with density 1/2, and prove it is optimal.
Keywords: domination, open-locating-dominating set, error-detection, triangular grid, density 
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     title = {Optimal error-detecting open-locating-dominating set on the infinite triangular grid},
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Jean, Devin; Seo, Suk J. Optimal error-detecting open-locating-dominating set on the infinite triangular grid. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 445-455. http://geodesic.mathdoc.fr/item/DMGT_2023_43_2_a8/