2024-10-172024-10-172007Balbuena, C., Cera López, M., Diánez Martínez, A.R., García Vázquez, P. y Marcote, X. (2007). On the restricted connectivity and superconnectivity in graphs with given girth. Discrete Mathematics, 307 (6), 659-667. https://doi.org/10.1016/j.disc.2006.07.016.0012-365X1872-681Xhttps://hdl.handle.net/11441/163746The restricted connectivity (G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity 1(G) is defined similarly, this time considering only vertices u in G − X, hence 1(G) (G). The minimum edge-degree of G is (G) = min{d(u) + d(v) − 2 : uv ∈ E(G)}, d(u) standing for the degree of a vertex u. In this paper, several sufficient conditions yielding 1(G) (G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17–31] and guaranteeing 1(G) = (G) = (G) under some additional constraints.application/pdf9 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/SuperconnectivityRestricted connectivityDiameterGirthinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.disc.2006.07.016