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arXiv · 2306.07862

New Optimal Results on Codes for Location in Graphs

Ville Junnila·Tero Laihonen·Tuomo Lehtilä
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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 $q\geq2$.

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Ville Junnila, Tero Laihonen, Tuomo Lehtilä. 2023-06-13. New Optimal Results on Codes for Location in Graphs. https://doi.org/10.46298/fi.11468

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