Fault-Tolerant Cycle Embedding in Cartesian Product Graphs: Edge-Pancyclicity and Edge-Bipancyclicity with Faulty Edges

A graph G is called k-edge-fault edge-bipancyclic (k-edge-fault edge-r-pancyclic) if after deleting k edges from G , every edge in the resulting graph lies in a cycle of every even length from 4 to |V(G)| (a cycle of every length from r to |V(G)| ), inclusively. In this paper, given two graphs G and H, which satisfy some specific properties, the edge-fault edge-bipancyclicity and edge-fault edge-r-pancyclicity (r is decided on the properties of G and H ) of Cartesian product graphs G x H are efficiently evaluated. The obtained results are applied to two multiprocessor systems, the nearest neighbor mesh hypercubes and generalized hypercubes, both of which belong to Cartesian product graphs.