On the connectivity of the direct product of graphs

In this note we show that the edge-connectivity lambda(G x H) of the direct product of graphs G and H is bounded below by min{lambda(G)|E(H)|,lambda(H)|E(G)|, delta(G x H)}and above by min{2 lambda(G)|E(H)|,2 lambda(H)|E(G)|, delta(G x H)}except in some special cases whenGis a relatively small bipartite graph, or both graphs are bipartite. Several upper bounds on thevertex-connectivity of the direct product of graphs are also obtained.