On the Extremal Zagreb Indices of $\mathit{\text{n}}$-Vertex Chemical Trees with Fixed Number of Segments or Branching Vertices

Let ${\mathcal{C}\mathcal{T}}_{n,k}$ and ${\mathcal{C}\mathcal{T}}_{n,b}^{\ast }$ be the classes of all $n$-vertex chemical trees with $k$ segments and $b$ branching vertices, respectively, where $3\le k\le n-1$ and $1\le b<\frac{n}{2}-1$. The solution of the problem of finding trees from the class ${\mathcal{C}\mathcal{T}}_{n,k}$ or ${\mathcal{C}\mathcal{T}}_{n,b}^{\ast }$, 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.