Geodesic
Vertex-Degree-Based Topological Indices Over Trees with Two Branching Vertices
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 399

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

Given a graph $G$ with $n$ vertices, a vertex-degree-based topological index is defined from a set of real numbers $\left\{ \varphi _{ij}\right\} $ as $TI\left( G\right) =\sum m_{ij}\left( G\right) \varphi _{ij}$, where $m_{ij}\left( G\right) $ is the number of edges between vertices of degree $i$ and degree $j$, and the sum runs over all $1\leq i\leq j\leq n-1$. Let $\Omega \left( n,2\right) $ denote the set of all trees with $n$ vertices and $2$ branching vertices. In this paper we give conditions on the number $\{\varphi_{ij}\}$ under which the extremal trees with respect to $TI$ can be determined. As a consequence, we find extremal trees in $\Omega \left( n,2\right) $ for several well-known vertex-degree-based topological indices.
Classification : 05C69, 05C35 05C05
Keywords: Vertex-degree-based topological indices, trees, branching vertices 
@article{KJM_2019_43_3_a4,
     author = {R. Cruz and C. A. Mar{\'\i}n and J. Rada},
     title = {Vertex-Degree-Based {Topological} {Indices} {Over} {Trees} with {Two} {Branching} {Vertices}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {399 },
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a4/}
}
TY  - JOUR
AU  - R. Cruz
AU  - C. A. Marín
AU  - J. Rada
TI  - Vertex-Degree-Based Topological Indices Over Trees with Two Branching Vertices
JO  - Kragujevac Journal of Mathematics
PY  - 2019
SP  - 399 
VL  - 43
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a4/
LA  - en
ID  - KJM_2019_43_3_a4
ER  - 
%0 Journal Article
%A R. Cruz
%A C. A. Marín
%A J. Rada
%T Vertex-Degree-Based Topological Indices Over Trees with Two Branching Vertices
%J Kragujevac Journal of Mathematics
%D 2019
%P 399 
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a4/
%G en
%F KJM_2019_43_3_a4
R. Cruz; C. A. Marín; J. Rada. Vertex-Degree-Based Topological Indices Over Trees with Two Branching Vertices. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 399 . http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a4/