New Optimal Results on Codes for Location in Graphs
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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× K_m of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs K_q□ K_q□ K_q with q≥2.
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