%0 Journal Article
%T On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Noureen, Sadia
%A Bhatti, Akhlaq Ahmad
%A Ali, Akbar
%D 2020
%\ 12/01/2020
%V 11
%N 4
%P 213-226
%! On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices
%K Chemical graph theory
%K topological index
%K Zagreb connection indices
%K extremal problem
%R 10.22052/ijmc.2020.240260.1514
%X The modified first Zagreb connection index $ZC_{1}^{*}$ for a graph $G$ is defined as $ZC_{1}^{*}(G)= \sum_{v\in V(G)}d_{v}\tau_{v}\,$, where $d_{v}$ is degree of the vertex $v$ and $\tau _{v}$ is the connection number of $v$ (that is, the number of vertices having distance 2 from $v$). By an $n$-vertex graph, we mean a graph of order $n$. A branching vertex of a graph is a vertex with degree greater than $2$. In this paper, the graphs with maximum and minimum $ZC_{1}^{*}$ values are characterized from the class of all $n$-vertex trees with a fixed number of branching vertices.
%U https://ijmc.kashanu.ac.ir/article_110827_9963a63de0e8366746c57fc8870654ad.pdf