In this paper, we broaden the understanding of the recently introduced concepts of solid-locating-dominating and self-locating-dominating codes in various graphs. In particular, we present the optimal, i.e., smallest possible, codes in the infinite triangular and king grids. Furthermore, we give optimal locating-dominating, self-locating-dominating and solid-locating-dominating codes in the direct product Kn×Km of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs Kq□Kq□Kq with q≥2.
@article{arxiv.2306.07862,
title = {New Optimal Results on Codes for Location in Graphs},
author = {Ville Junnila and Tero Laihonen and Tuomo Lehtilä},
journal= {arXiv preprint arXiv:2306.07862},
year = {2025}
}