(untitled) (Communications in Mathematical Research, 2020)
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 AZI(G)=_uvE(G)(d_ud_vd_u+d_v-2)^3, and the atom-bond connectivity index (ABC index for short) of a graph G is defined asABC(G)=_uvE(G)d_u+d_v-2d_ud_v , where d_u and d_v 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.