Geodesic
Graph connectivity and Wiener index
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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I. Gutman; S. Zhang. Graph connectivity and Wiener index. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1. http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a0/