The hull number of strong product graphs

For a connected graph G with at least two vertices and S a subset of vertices, the convex hull [S]G is the smallest convex set containing S. The hull number h(G) is the minimum cardinality among the subsets S of V (G) with [S]G = V (G). Upper bound for the hull number of strong product G⊠H of two graphs G and H is obtainted. Improved upper bounds are obtained for some class of strong product graphs. Exact values for the hull number of some special classes of strong product graphs are obtained. GraphsG andH for which h(G⊠H) = h(G)h(H) are characterized.