An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

Abstract

For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of i∈VG. For α∈R, if ϕ=(dxdy)α (resp. ϕ=(dx+dy)α), the index is called the general product-connectivity Rα (resp. general sum-connectivity SCIα) index. In this paper, by formulating an optimization problem, we determine the value(s) of α, for which the linear/multiple correlation coefficient of Rα and SCIα with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area.

Keywords

• chemical graph theory
• graph
• benzenoid hydrocarbon
• boiling point
• enthalpy of formation
• general sum-connectivity index