Geodesic
Graph connectivity and Wiener index
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 
@article{BASS_2006_31_1_a0,
     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 - 5},
     year = {2006},
     volume = {31},
     number = {1},
     zbl = {1150.05327},
     url = {http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a0/}
}
TY  - JOUR
AU  - I. Gutman
AU  - S. Zhang
TI  - Graph connectivity and Wiener index
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2006
SP  - 1 
EP  -  5
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a0/
ID  - BASS_2006_31_1_a0
ER  - 
%0 Journal Article
%A I. Gutman
%A S. Zhang
%T Graph connectivity and Wiener index
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2006
%P 1 - 5
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a0/
%F BASS_2006_31_1_a0
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/