Geodesic
Minimum Eccentric Connectivity Index for Graphs With Fixed Order and Fixed Number of Pendant
Yugoslav journal of operations research, Tome 29 (2019) no. 2, p. 193

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

The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product $d_G(v) e_G(v)$, where $d_G(v)$ is the degree of $v$ in $G$ and $e_G(v)$ is the maximum distance between $v$ and any other vertex of $G$. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order $n$. Then, given two integers $n$ and $p$ with $p \le n-1$, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order $n$ with $p$ pendant vertices.
Classification : 05C35, 05C40
Keywords: Extremal Graph Theory, Eccentric Connectivity Index, Pendant Vertices 
@article{YJOR_2019_29_2_a2,
     author = {Gauvain Devillez and Alain Hertz and Hadrien M\'elot and Pierre Hauweele},
     title = {Minimum {Eccentric} {Connectivity} {Index} for {Graphs} {With} {Fixed} {Order} and {Fixed} {Number} of {Pendant}},
     journal = {Yugoslav journal of operations research},
     pages = {193 },
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2019_29_2_a2/}
}
TY  - JOUR
AU  - Gauvain Devillez
AU  - Alain Hertz
AU  - Hadrien Mélot
AU  - Pierre Hauweele
TI  - Minimum Eccentric Connectivity Index for Graphs With Fixed Order and Fixed Number of Pendant
JO  - Yugoslav journal of operations research
PY  - 2019
SP  - 193 
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/YJOR_2019_29_2_a2/
LA  - en
ID  - YJOR_2019_29_2_a2
ER  - 
%0 Journal Article
%A Gauvain Devillez
%A Alain Hertz
%A Hadrien Mélot
%A Pierre Hauweele
%T Minimum Eccentric Connectivity Index for Graphs With Fixed Order and Fixed Number of Pendant
%J Yugoslav journal of operations research
%D 2019
%P 193 
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/YJOR_2019_29_2_a2/
%G en
%F YJOR_2019_29_2_a2
Gauvain Devillez; Alain Hertz; Hadrien Mélot; Pierre Hauweele. Minimum Eccentric Connectivity Index for Graphs With Fixed Order and Fixed Number of Pendant. Yugoslav journal of operations research, Tome 29 (2019) no. 2, p. 193 . http://geodesic.mathdoc.fr/item/YJOR_2019_29_2_a2/