University of KashanIranian Journal of Mathematical Chemistry2228-648912320210901On the trees with given matching number and the modified first Zagreb connection index12713811151510.22052/ijmc.2021.242169.1554ENSadiaNoureenDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanDepartment of Mathematics, Faculty of Science, University of Gujrat, Gujrat, PakistanAkhlaqAhmad BhattiDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanJournal Article20210329The modified first Zagreb connection index ZC<sup>∗</sup><sub>1</sub> for a graph G is defined as ZC<sup>∗</sup><sub>1</sub> (G) = sum v∈V (G) d<sub>v</sub>τ<sub>v</sub> , where d<sub>v</sub> is the degree of the vertex v and τ<sub>v</sub> denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let T<sub>n,α</sub> be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.https://ijmc.kashanu.ac.ir/article_111515_484b409936d065a89799b3a7e36adc56.pdf