### Abstract

A path in G is a hamiltonian path if it contains all vertices of G. A graph G is hamiltonian connected if there exists a hamiltonian path between any two distinct vertices of G. The degree of a vertex u in G is the number of vertices of G adjacent to u. We denote by B(G) the minimum degree of vertices of G. A graph G is conditional k edge-fault tolerant hamiltonian connected if G - F is hamiltonian connected for every F C E(G) with |F| <= k and S(G - F) >= 3. The conditional edge-fault tolerant hamiltonian connectivity HCe3(G) is defined as the maximum integer k such that G is k edge-fault tolerant conditional hamiltonian connected if G is hamiltonian connected and is undefined otherwise. Let n >= 4. We use K-n to denote the complete graph with n vertices. In this paper, we show that HCe3(K-n) = 2n - 10 for n is not an element of {4, 5, 8, 10}, HCe3 (K-4) = 0, HCe3 (K-5) = 2, HCe3(K-8) = 5, and HCe3(K-10) = 9. (c) 2009 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 585-588 |

Number of pages | 4 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 12 |

DOIs | |

State | Published - 31 May 2009 |

### Keywords

- Complete graph; Hamiltonian; Hamiltonian connected; Fault tolerance

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## Cite this

Ho, T-Y., Shih, Y-K., Tan, J-M., & Hsu, L-H. (2009). Conditional fault hamiltonian connectivity of the complete graph.

*Information Processing Letters*,*109*(12), 585-588. https://doi.org/10.1016/j.ipl.2009.02.008