Dankelmann, Peter; Oellermann, Ortrud R. Bounds on the average connectivity of a graph. (English) Zbl 1021.05062 Discrete Appl. Math. 129, No. 2-3, 305-318 (2003). This paper proposes the new concept of average connectivity of a graph, defined to be the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting theses vertices. The authors 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 relationship between the clique number and chromatic number of a graph are also established. Reviewer: Jun-Ming Xu (Hefei) Cited in 1 ReviewCited in 8 Documents MSC: 05C40 Connectivity 05C35 Extremal problems in graph theory Keywords:average degree; planar graphs; Cartesian products; chromatic number PDFBibTeX XMLCite \textit{P. Dankelmann} and \textit{O. R. Oellermann}, Discrete Appl. Math. 129, No. 2--3, 305--318 (2003; Zbl 1021.05062) Full Text: DOI References: [1] Bagga, K. S.; Beineke, L. W.; Pippert, R. E.; Lipman, M. J., A classification scheme for vulnerability and reliability parameters of graphs, Math. Comput. Modelling, 17, 13-16 (1993) · Zbl 0800.68628 [2] Beineke, L. W.; Oellermann, O. R.; Pippert, R. E., The average connectivity of a graph, Discrete Math., 252, 31-45 (2002) · Zbl 1002.05040 [3] Chartrand, G.; Oellermann, O. R., Applied and Algorithmic Graph Theory (1993), McGraw-Hill: McGraw-Hill New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.