An optimal locating-dominating set in the infinite triangular grid

: Honkala I

Publisher: ELSEVIER SCIENCE BV

: 2006

: Discrete Mathematics

: DISCRETE MATHEMATICS

: DISCRETE MATH

: 306

: 21

: 2670

: 2681

: 12

: 0012-365X

DOI: https://doi.org/10.1016/j.disc.2006.04.028

Assume that G = (V, E) is an undirected graph, and C subset of V. For every v is an element of V, we denote by I (v) the set of all elements of C that are within distance one from v. If all the sets I (v) for v is an element of V\C are non-empty, and pairwise different, then C is called a locating-dominating set. The smallest possible density of a locating-dominating set in the infinite triangular grid is shown to be (13)/(57) (c) 2006 Elsevier B.V. All rights reserved.

Mathematics