2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225584A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect) dominating set in $G$ if each vertex $v$ of $G\setminus S$ is adjacent to only one vertex ($d_v\in\{1,2\}$ vertices) of $S$. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol $\{3,6\}$ and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets $S$ with induced components of the form $K_ν$, where $ν\in\{1,2,3\}$ depends only on $S$.20 pages, 9 figures, 5 arraysCombinatoricsInformation Theory05C69, 68R10text