Abstract
Let Gamma(n,k) be the class of all graphs with n >= 3 vertices and k >= 2 vertex connectivity. Denote by Upsilon(n,beta) the family of all connected graphs with n >= 4 vertices and matching number beta where 2 <= beta <= left perpendicalar n/2 right perpendicalar In the classes of graphs Gamma(n,k) and Upsilon(n,beta), the elements having maximum augmented Zagreb index are determined.