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 \(M ⊆ V(G)\) 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 \(x, y ∈ V(G)\) are \(M\)-visible, meaning there exists a shortest \(x, y\)-path in \(G\) that does not pass through any vertex of \(M \{x, y\}\). 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.