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

Rennan Dantas (1) , Frédéric Havet (2) , Rudini M Sampaio (1)

1 ParGO - Parallelism, Graphs and Optimization Research Group
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications

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.

Domaines: Mathématique discrète [cs.DM]

Rennan Dantas, Frédéric Havet, Rudini M Sampaio. Identifying codes for infinite triangular grids with a finite number of rows. Bordeaux Graph Workshop 2016, Nov 2016, Bordeaux, France. ⟨hal-01411109⟩