For a given graph G, the general position problem asks for the largest size of a 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 cardinality 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 Sierpiński triangle graphs.
