2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130150We study vertex colorings of the square $G^2$ of an outerplanar graph $G$. We find the optimal bound of the inductiveness, chromatic number and the clique number of $G^2$ as a function of the maximum degree $Δ$ of $G$ for all $Δ\in \nats$. As a bonus, we obtain the optimal bound of the choosability (or the list-chromatic number) of $G^2$ when $Δ\geq 7$. In the case of chordal outerplanar graphs, we classify exactly which graphs have parameters exceeding the absolute minimum.24 pages, 17 figuresCombinatorics05C15text