Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index

Let G be a simple connected graph with vertex set V (G) and edge set E (G). The augmented Zagreb index of a graph G is defined as∑( dudv )3 AZ I (G)=, du+dv?2 uv∈E(G) and the atom-bond connectivity index (ABC index for short) of a graph G is defined as∑√du+dv?2 ABC(G)=, dudv uv∈E(G) where du and dv denote the degree of vertices u and v in G, respectively. In this paper, trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined, respectively.