The augmented Zagreb index, vertex connectivity and matching number of graphs

Document Type: Research Paper

Authors

1 Department of Mathematics, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.

2 Department of Mathematics, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.and Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates.

Abstract

‎Let $\Gamma_{n,\kappa}$ be the class of all graphs with $n\geq3$ vertices and $\kappa\geq2$ vertex connectivity‎. ‎Denote by $\Upsilon_{n,\beta}$ the family of all connected graphs with $n\geq4$ vertices and matching number $\beta$ where $2\leq\beta\leq\lfloor\frac{n}{2}\rfloor$‎. ‎In the classes of graphs $\Gamma_{n,\kappa}$ and $\Upsilon_{n,\beta}$‎, ‎the elements having maximum augmented Zagreb index are determined.

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Main Subjects


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