Complexity results on k-independence in some graph products

For a positive integer k , a subset S of vertices of a graph G is k -independent if each vertex in S has at most k − 1 neighbors in S . We consider k -independent sets in two graph products: Cartesian and complementary prism. We show that the problem of determining k -independence remains NP-complete even for Cartesian products and complementary prisms. Furthermore, we present results on k -independence in the Cartesian product of two paths, known as grid graphs.