The general position problem on Kneser graphs and on some graph operations

A vertex subset \(S\) of a graph \(G\) is a general position set of \(G\) if no vertex of \(S\) lies on a geodesic between two other vertices of \(S\). The cardinality of a largest general position set of \(G\) is the general position number (gp-number) \({\rm gp}(G)\) of \(G\). The gp-number is determined for some families of Kneser graphs, in particular for \(K(n,2)\) and \(K(n,3)\). A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.