## Abstract

Let G be a connected graph and k∈N. The k-edge-fault diameter of G is defined as the largest diameter of the graphs arising from G by deleting k edges. In this paper we show that the k-edge-fault diameter of a (k+1)-edge connected graph of order n not containing a 4-cycle cannot exceed [Formula presented], and we construct graphs that show that for k+1 a prime power this bound is close to optimal if k is large. For the special case k=2 we improve the above bound and obtain the sharp bound [Formula presented] on the 2-edge-fault diameter of 3-edge-connected graphs of order n not containing a 4-cycle.

Original language | English |
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Article number | 113678 |

Journal | Discrete Mathematics |

Volume | 347 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2024 |

## Keywords

- Diameter
- Diameter vulnerability
- Edge-fault diameter
- Fault diameter
- Fault tolerant diameter

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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