On General Position Sets in Cartesian Products

Abstract The general position number $$\mathrm{gp}(G)$$ gp ( G ) of a connected graph G is the cardinality largest set S vertices such that no three distinct from lie on common geodesic; sets are refereed to as gp-sets . cylinders $$P_r\,\square \,C_s$$ P r □ C s deduced. It proved $$\mathrm{gp}(C_r\,\square \,C_s)\in \{6,7\}$$ ∈ { 6 , 7 } whenever $$r\ge s \ge 3$$ ≥ 3 , $$s\ne 4$$ ≠ 4 and 6$$ A probabilistic lower bound Cartesian powers achieved. Along way formula for in \,P_s$$ where $$r,s\ge 2$$ 2 also determined.