The induced path number of complementary prisms

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In this paper, we study the induced path number of complementary prisms of complete graphs, stars, paths, and cycles.