The basis number of the cartesian product of certain classes of graphs

Abstract

In this paper we prove that the basis number of the Cartesian product of paths, cycles and theta graphs with Tenets is exactly 3. However, if we apply Theorem 4.1 of Ali and Marougi [3], which gives a general upper bound of the Cartesian product of disjoint connected graphs, we find that the basis number of these graphs is less than or equal to 4.