Edge Fault Tolerance of Cartesian Product Graphs on Super Restricted Edge Connectivity.

The cartesian product is a very effective method for designing large-scale interconnection networks. The super-lambda' property is an index to measure the reliability of networks. Let G = (V, E) be a connected graph. An edge set S subset of E is a restricted edge cut if G - S is disconnected and every component of G - S has at least two vertices. A graph G is super-lambda' if every minimum restricted edge cut of G isolates one edge. Fault tolerance of networks is an important issue. The edge fault tolerance S-lambda'(G) of a super-lambda' graph G on the super-lambda' property is the maximum integer m for which G - S is still super-lambda' for any edge set S subset of E with vertical bar S vertical bar <= m. In this paper, we give the lower and upper bounds on S-lambda'(G) for the cartesian product of graphs. More refined bounds on S-lambda'(G) are obtained for the cartesian product of regular graphs. In particular, exact values of S-lambda'(G) are determined for some special classes of the cartesian product graphs. For example, if G(i) is a connected regular graph with delta(i)= delta(G(i)) = lambda(G(i)) >= 4 for i = 1, 2,...n, then Sigma(n)(i=1) delta(i)-2 <= S-lambda'(G(1) x G(2) x...x G(n)) <= Sigma(n)(i=1) delta(i)-1.