Theoretical analysis reveals optimal locating-dominating codes across infinite grids, direct products, and Hamming graphs, highlighting minimal configurations for network monitoring.
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.
No takes yet. Share an insight, caveat, or question.
Junnila et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: