This paper showed the pancyclicity of Cartesian product graphs with faulty edges.This paper showed the bipancyclicity of Cartesian product graphs with faulty edges.Determining the edge-fault pancyclicity (bipancyclicity) of NQ m r , ? , m 1 efficiently.Determining the edge-fault pancyclicity (bipancyclicity) of GQ m r , ? , m 1 efficiently. Let r? 4 be an even integer. Graph G is r-bipancyclic if it contains a cycle of every even length from r to 2 ? n ( G ) 2 ? , where n ( G ) is the number of vertices in G. A graph G is r-pancyclic if it contains a cycle of every length from r to n ( G ) , where r ? 3 . A graph is k-edge-fault Hamiltonian if, after deleting arbitrary k edges from the graph, the resulting graph remains Hamiltonian. The terms k-edge-fault r-bipancyclic and k-edge-fault r-pancyclic can be defined similarly. Given two graphs G and H, where n ( G ) , n ( H ) ? 9, let k 1 , k 2 ? 5 be the minimum degrees of G and H, respectively. This study determined the edge-fault r-bipancyclic and edge-fault r-pancyclic of Cartesian product graph G × H with some conditions. These results were then used to evaluate the edge-fault pancyclicity (bipancyclicity) of NQ m r , ? , m 1 and GQ m r , ? , m 1 .
['Chia-Wen Cheng', 'Sun-Yuan Hsieh']
Edge-fault-tolerant pancyclicity and bipancyclicity of Cartesian product graphs with faulty edges