Edge‐superconnectivity of cages
X. Marcote, Camino Balbuena · Networks · 2003
Abstract A graph with minimum degree δ is said to be edge‐superconnected if each minimum edge‐cut consists of all the edges incident with some vertex (so λ = δ). A smallest δ‐regular graph G with girth g is said to be a (δ, g)‐cage. We show that every (δ, g)‐cage with odd girth is edge‐superconnected. This result strengthens one obtained by Wang et al. (λ = δ for every such cage) and supports the conjecture of Fu et al. that all (δ, g)‐cages are δ‐connected. © 2003 Wiley Periodicals, Inc.