Mutual-visibility and general position sets in Sierpi\'nski triangle graphs

For a given graph $G$, the general position problem asks for the largest set of vertices $M \subseteq V(G)$ such that no three distinct vertices of $M$ belong to a common shortest path in $G$. A relaxation of this concept is based on the condition that two vertices $x, y \in V(G)$ are $M$-visible, meaning there exists a shortest $x, y$-path in $G$ that does not pass through any vertex of $M \setminus \{x, y\}$. If every pair of vertices in $M$ is $M$-visible, then $M$ is called a mutual-visibility set of $G$. The size of the largest mutual-visibility set of $G$ is called the mutual-visibility number of $G$. Some well-known variations of this concept consider the total, outer, and dual mutual-visibility sets of a graph. We present results on the general position problem and the various mutual-visibility problems in Sierpi\'nski triangle graphs.