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

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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 
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     author = {R. Cruz and C. A. Mar{\'\i}n and J. Rada},
     title = {Vertex-Degree-Based {Topological} {Indices} {Over} {Trees} with {Two} {Branching} {Vertices}},
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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/