New Optimal Results on Codes for Location in Graphs
Abstract
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 $K_n\times K_m$ of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs $K_q\square K_q\square K_q$ with $q\geq2$.
Fields of Study & Subjects
Coding theory and cryptography
Cooperative Communication and Network Coding
Publication details
- Journal / source
- Fundamenta Informaticae
- Publisher
- Centre pour la Communication Scientifique Directe (CCSD)
- Volume
- Volume 196, Issue 1
- Publication date
- 20 August 2026
- Language
- EN