فهرست نشریات علمی دسترسی آزاد ایران

‎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.