University of KashanIranian Journal of Mathematical Chemistry2228-648911420201201On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices21322611082710.22052/ijmc.2020.240260.1514ENSadiaNoureenNational University of Computer and Emerging Sciences, Lahore, PakistanAkhlaq AhmadBhattiNational University of Computer and
Emerging Sciences, Lahore, PakistanAkbarAliUniversity of Hail, Hail, Saudi Arabia0000-0001-8160-4196Journal Article20200830The 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.https://ijmc.kashanu.ac.ir/article_110827_9963a63de0e8366746c57fc8870654ad.pdf