Complexity results on k-independence in some graph products

For a positive integer k, a subset S of vertices of a graph G=(V,E) 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 k-independence remains NP-complete even for Cartesian products and complementary prisms. Furthermore, we present results on k-independence in grid graphs, which is a Cartesian product of two paths.