Connectivity of Cartesian product graphs

Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graphGi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1×G2) 1+ 2 and (G1×G2) 1+ 2. This paper improves these results by proving that (G1×G2) min{ 1+ 2, 2+ 1} and (G1×G2)= min{ 1+ 2, 1v2, 2v1} ifG1 andG2 are connected undirected graphs; (G1×G2) min{ 1+ 2, 2+ 1, 2 1+ 2, 2 2+ 1} if G1 and G2 are strongly connected digraphs. These results are also generalized to the Cartesian products of n ( 3) connected graphs and n strongly connected digraphs, respectively. © 2005 Elsevier B.V. All rights reserved.