Bounds on the average connectivity of a graph Original Research Article

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.