Geodesic
Graph connectivity and Wiener index
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006), p. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 $K_1$ .
DOI : 10.2298/BMAT0631001G
Classification : 05C12 05C40 05C35
Keywords: graph connectivity, vertex-connectivity, edge-connectivity, Wiener index, extremal graphs 
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     author = {I. Gutman and S. Zhang},
     title = {Graph connectivity and {Wiener} index},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {1 },
     year = {2006},
     volume = {31},
     doi = {10.2298/BMAT0631001G},
     zbl = {1150.05327},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0631001G/}
}
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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), p. 1 . doi: 10.2298/BMAT0631001G

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