Abstract
Let CT n,k and CTn,b* be the classes of all n-vertex chemical trees with k segments and b branching vertices, respectively, where 3 <= k <= n -1 and 1 <= b < n/2 - 1. The solution of the problem of finding trees from the class CT (n,k) or CTn,b*, with the minimum first Zagreb index or minimum second Zagreb index follows directly from the main results of [MATCH Commun. Math. Comput. Chem. 72 (2014) 825-834] or [MATCH Commun. Math. Comput. Chem. 74 (2015) 57-79]. In this paper, the chemical trees with the maximum first/second Zagreb index are characterized from each of the aforementioned graph classes. Along the way, some similar results concerning the reduced second Zagreb index are also discussed at the end of this paper.