The pre-hull number and lexicographic product

Recently the invariant (copoint) pre-hull number ph(G) of a graph GG that measures the nonconvexity of a convex space was introduced in [15]. We introduce a similar invariant called the convex pre-hull number which is a natural upper bound for the copoint pre-hull number and consider in this work both on the lexicographic product of graphs. We present exact values with respect to properties of the factors.