Bounds on the average connectivity of a graph

Authors:
Peter Dankelmann;Ortrud R. Oellermann
Affiliations:
University of Natal, Durban 4014, South Africa;The University of Winnipeg, 515 Portage Avenue, Winnipeg, Man, R3B 2E9, Canada
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

In this paper, we consider the concept of the average connectivity of a graph, defined to be the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. We establish sharp bounds for this parameter in terms of the average degree and improve one of these bounds for bipartite graphs with perfect matchings. Sharp upper bounds for planar and outerplanar graphs and cartesian products of graphs are established. Nordhaus-Gaddum-type results for this parameter and relationships between the clique number and chromatic number of a graph are also established.