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 $q\geq2$.
From: Tuomo Lehtilä [view email]
[v1]
Tue, 13 Jun 2023 15:48:09 UTC (28 KB)
[v2]
Fri, 9 May 2025 16:11:40 UTC (28 KB)
[v3]
Mon, 17 Aug 2026 09:15:34 UTC (29 KB)
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