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On average connectivity of the strong product of graphs

 

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Autor: Abajo Casado, María Encarnación
Moreno Casablanca, Rocío
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Fecha: 2013
Publicado en: Discrete Applied Mathematics, 161 (18), 2795-2801.
Tipo de documento: Artículo
Resumen: 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.
Cita: Abajo Casado, M.E., Moreno Casablanca, R., Diánez Martínez, A.R. y García Vázquez, P. (2013). On average connectivity of the strong product of graphs. Discrete Applied Mathematics, 161 (18), 2795-2801.
Tamaño: 510.3Kb
Formato: PDF

URI: https://hdl.handle.net/11441/69459

DOI: 10.1016/j.dam.2013.06.005

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