فهرست نشریات علمی دسترسی آزاد ایران

‎Let $G$ be a graph with vertex set $V\left(G \right)$‎. ‎The vertex-degree function index $H_{f}\left(G \right) $ is defined on $G$ as‎: ‎$H_{f}\left(G \right) =\sum_{u\in V\left(G \right)}f\left(d_{u} \right)‎,$‎where $f\left(x \right) $ is a function defined on positive real numbers‎. ‎Our main concern in this paper is to study $H_{f}$ over the set $\mathcal{T}_{n}$ of trees with $n$ vertices‎, ‎over the set $\mathcal{T}_{n,k}$ of trees with $n$ vertices and $k$ branching vertices‎, ‎and over the set $\mathcal{T}^{p}_{n}$ of trees with $n$ vertices and $p$ pendant vertices‎. ‎Namely‎, ‎we will show in each of these sets of trees that it is possible via branching operations to construct a strictly monotone sequence of trees that reaches the extremal values of $H_{f}$‎, ‎when $f\left( x+1\right)-f\left( x\right) $ is a strictly increasing function‎.