The Diameter Variability of the Product Graphs

The diameter of a graph can be affected by the addition or the deletion of some edges. In [3], we have studied the diameter variability of the Cartesian product of graphs. In this paper, we discuss about two fundamental products, strong and lexicographic products of graphs, whose diameter increases (decreases) by the deletion (addition) of a single edge. The problems of minimality and maximality of the product graphs with respect to its diameter are also solved. These problems are motivated by the fact that these graph products are good interconnection networks.