On average connectivity of the strong product of graphs
The average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connec...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/69459 |
| Acceso en línea: | https://hdl.handle.net/11441/69459 https://doi.org/10.1016/j.dam.2013.06.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Average connectivity Strong Product Graphs Maximally connected graphs Average degree |
| Sumario: | The average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity and the average connectivity are upper bounded by the minimum degree δ(G) and the average degree d(G) of G, respectively. In this paper the average connectivity of the strong product G1 G2 of two connected graphs G1 and G2 is studied. A sharp lower bound for this parameter is obtained. As a consequence, we prove that κ(G1 G2) = d(G1 G2) if κ(Gi) = d(Gi), i = 1, 2. Also we deduce that κ(G1 G2) = δ(G1 G2) if κ(Gi) = δ(Gi), i = 1, 2. |
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