Bulletin: Classe des sciences mathematiques et natturalles 2006 Volume 133, Issue 31, Pages: 1-5
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Graph connectivity and Wiener index
Gutman I., Zhang S.
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 Kk + (K1 U Kn-k-1), the graph obtained by connecting all vertices of the complete graph Kk with all vertices of the graph whose two components are Kn-k-1 and K1. AMS Mathematics Subject Classification (2000): 05C12, 05C40 05C35.
Keywords: graph connectivity, vertex-connectivity, edge-connectivity, Wiener index, extremal graphs
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