On the Multiplicative‎ ‎Reformulated‎ ‎First‎ ‎Zagreb Index of n-Vertex‎ ‎Trees ‎ ‎with Respect to Matching Number

‎The multiplicative first Zagreb index is the product of the square of the degree of vertices in a graph $\mathbb{G}‎. ‎The multiplicative reformulated first Zagreb index is defined as \prod_{1,e}(\mathbb{G})= \prod_{x_{1}x_{2}\in E(\mathbb{G})}(d_{\mathbb{G}}(x_{1})+d_{\mathbb{G}}(x_{1})-2)^{2}‎, ‎where E(\mathbb{G}) is the edge set of a graph \mathbb{G}and d_{\mathbb{G}}(x_{1}) is the degree of a vertex x_{1} in a graph \mathbb{G}‎. ‎In this paper‎, ‎we characterize the minimum and maximum trees and unicyclic graphs with respect to matching and perfect matching using this graph invariant \prod_{1,e}(\mathbb{G}) among the collection of all n-vertex graphs‎.