Abstract: Let G=(V, E) be a simple graph with vertex set V and edge set E. A k-clique-coloring of G is a mapping $\phi: V\rightarrow {1, 2, ...,  k},  such that no maximal clique of size at least two is monochromatic. The clique-coloring number of G is the smallest k for which c is a k-clique-coloring of G.  In this paper we investigate the clique-coloring numbers of Cartesian product, Kronecker product, strong product and lexicographical product of two graphs.

Key words: clique coloring, Cartesian product, Kronecker product, strong product, lexicographical product