Vulnerability of super extra edge-connected graphs

Chia-Wen Cheng (1) , Sun-Yuan Hsieh (1) , Ralf Klasing (2)

1 NCKU - National Cheng Kung University
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Mots clés: Edge-connectivity; extra edge-connectivity; fault tolerance; persistence of networks; super extra edge-connectivity

Domaines: Réseaux et télécommunications [cs.NI]

Chia-Wen Cheng, Sun-Yuan Hsieh, Ralf Klasing. Vulnerability of super extra edge-connected graphs. Journal of Computer and System Sciences, 2020, 108, pp.1-9. ⟨10.1016/j.jcss.2019.07.002⟩. ⟨hal-02397462⟩