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 $q\geq2$.

翻译：本文深化了对近期提出的图论中固态定位-支配码与自定位-支配码概念的理解。具体而言，我们在无限三角网格与王网格中给出了最优（即最小可能）的码。此外，我们在完全图的直积 $K_n\times K_m$ 上给出了最优的定位-支配码、自定位-支配码及固态定位-支配码。我们还针对 $q\geq2$ 的汉明图 $K_q\square K_q\square K_q$ 给出了最优的固态定位-支配码。