On the maximum augmented Sombor index of molecular trees with a perfect matching

Let G be a graph with edge set E(G).Recently, Das, Gutman and Ali introduced a new vertex-degree-based topological index, called the augmented Sombor index of G, defined aswhere d(u) denotes the degree of vertex u.In this paper, we establish an upper bound on the augmented Sombor index for molecular trees with a given perfect matching and characterize the corresponding extremal graphs.