Extremal values of vertex-degree-based topological indices over hexagonal systems with fixed number of vertices

Let G be a graph with n   vertices. A vertex-degree-based topological index is defined from a set of real numbers {ψij}ψij asTIG=∑1⩽i⩽j⩽n-1mijψijwhere mijmij is the number of edges of G connecting a vertex of degree i with a vertex of degree j. Many of the well-known topological indices are particular cases of this expression, including all Randić-type connectivity indices. In this work we determine extremal values for TI   over the set HSnHSn of hexagonal systems with a fixed number of vertices.