General position sets in strong products with paths and cycles

Abstract

We study general position sets in strong products involving paths and cycles. For every connected graph $H$ and every $s\ge 2$, we prove that gp$(P_s \boxtimes H)=2$gp$(H)$. We also determine the corresponding values when the path is replaced by $C_4$, $C_5$, or $C_6$, and establish a general upper bound for gp$(C_s \boxtimes H)$. These results are then applied to strong products of two cycles. We determine several exact values, construct infinite families attaining the general upper bound, and provide counterexamples to the conjectured multiplicativity of the general position number under the strong product.