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

Abstract

‎Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity‎. ‎Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$‎. ‎In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$‎, ‎the elements having maximum augmented Zagreb index are determined.