Concerning the number of maximal general position sets of connected graphs

A set X of vertices of a connected graph G having no three vertices that lie in a same geodesic is a general position set of G. A general position set in G is maximal if it is not properly contained in any other general position set. We are interested in this work into counting the number of maximal general position sets that a given connected graph has. In particular, we consider such counting for classical graph classes including grids, trees and hypercubes.