Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices

Document Type : Research Paper

Authors
Sadia Noureen 1
Akhlaq Ahmad Bhatti 1
Akbar Ali 2
1 National University of Computer and Emerging Sciences, Lahore, Pakistan
2 University of Hail, Hail, Saudi Arabia
10.22052/ijmc.2020.240260.1514
Abstract
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.
Keywords
chemical graph theory
topological index
Zagreb connection indices
extremal problem

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Iranian Journal of Mathematical Chemistry
Volume 11, Issue 4
Autumn 2020
Pages 213-226