On the hull sets and hull number of the cartesian product of graphs

AbstractFor a connected graph G, the convex hull of a subset C of V(G) is defined as the smallest convex set in G containing C. A subset C of V(G) is a hull set in G if the convex hull of C is V(G). The cardinality of a minimum hull set in G is called the hull number of G. Chartrand, Harary and Zhang (2000) presented the hull number of the Cartesian product of a nontrivial connected graph and K2. In this paper, we give the hull number of the Cartesian product of any two connected graphs