## Abstract

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 _{k1}, _{k2}≥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}_{mr},⋯,_{m1} and _{GQ}_{mr},⋯,_{m1}.

Original language | English |
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Pages (from-to) | 767-781 |

Number of pages | 15 |

Journal | Journal of Computer and System Sciences |

Volume | 82 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2016 Aug 1 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics