Mutual-visibility and general position sets in Sierpiński triangle graphs

Abstract: 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.