EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIII, No. 31, pp. 1–5 (2006)

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Graph connectivity and Wiener index

I. Gutman and S. Zhang

Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, P. R. China

Abstract: The graphs with a given number $n$ of vertices and given (vertex or edge) connectivity $k$ , having minimum Wiener index are determined. In both cases this is $K_k+(K_1 \cup K_{n-k-1})$ , the graph obtained by connecting all vertices of the complete graph $K_k$ with all vertices of the graph whose two components are $K_{n-k-1}$ and $K_1$ .

Keywords: graph connectivity, vertex–connectivity, edge–connectivity, Wiener index; extremal graphs

Classification (MSC2000): 05C12, 05C40, 05C35

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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