On the restricted connectivity and superconnectivity in graphs with given girth
The 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 m...
| Autores: | , , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163746 |
| Acceso en línea: | https://hdl.handle.net/11441/163746 https://doi.org/10.1016/j.disc.2006.07.016 |
| Access Level: | acceso abierto |
| Palabra clave: | Superconnectivity Restricted connectivity Diameter Girth |
| Sumario: | The 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. |
|---|