On General Position Sets in Cartesian Products

Abstract

The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gpsets of G. The general position number of cylinders Pr square Cs is deduced. It is proved that gp(Cr square C-s). {6, 7} whenever r >= s = 3, s >=not equal 4, and r >= 6. A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in Pr square Ps, where r, s >= 2, is also determined.