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

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Faculty of Science‎, University of Gujrat‎, ‎Gujrat‎, ‎Pakistan

10.22052/ijmc.2024.253967.1793

Abstract

‎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.

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References

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Iranian Journal of Mathematical Chemistry
Volume 15, Issue 3
September 2024
Pages 203-225

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