Year: 2026
Type: preprint
Abstract: We study two variants of location-domination in infinite triangular grids which allow locating up to $\ell$ vertices simultaneously. A locating-dominating code $S$ is a dominating vertex set such that every vertex outside of it has a unique neighborhood within the code $S$. As this neighborhood is unique, we may use it as an identifier for locating the considered vertex outside of the vertex set. With the variants we study, we may also locate sets of vertices instead of only single vertices. In particular, we obtain the exact minimum densities of these types of sets in the infinite triangular grid for every value of $\ell$.
Source: arXiv (Cornell University)
Authors: Das, Soura Sena, Lehtilä, Tuomo, Sen, Sagnik
Institution: Indian Institute of Technology Dharwad
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G3941552351
OpenAlex ID: W7220453171