## Abstract

Edge connectivity is a crucial measure of the robustness of a network. Several edge connectivity variants have been proposed for measuring the reliability and fault tolerance of networks under various conditions. Let G be a connected graph, S be a subset of edges in G, and k be a positive integer. If G−S is disconnected and every component has at least k vertices, then S is a k-extra edge-cut of G. The k-extra edge-connectivity, denoted by λ_{k}(G), is the minimum cardinality over all k-extra edge-cuts of G. If λ_{k}(G) exists and at least one component of G−S contains exactly k vertices for any minimum k-extra edge-cut S, then G is super-λ_{k}. Moreover, when G is super-λ_{k}, the persistence of G, denoted by ρ_{k}(G), is the maximum integer m for which G−F is still super-λ_{k} for any set F⊆E(G) with |F|≤m. Previously, bounds of ρ_{k}(G) were provided only for k∈{1,2}. This study provides the bounds of ρ_{k}(G) for k≥2.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Journal of Computer and System Sciences |

Volume | 108 |

DOIs | |

Publication status | Published - 2020 Mar |

## All Science Journal Classification (ASJC) codes

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