Harmonic Index of Chemical Trees with Given Number of Vertices of Maximum Degree

Abstract

Graph theory is a major mathematical discipline that provides a powerful framework to solve complex problems that can be modeled in the form of graphs. Its applications are diversified into a number of scientific fields. It is widely used in analyzing the structure of molecules and predicting their physicochemical properties. One of the major concepts used to quantify these properties is topological indices. A topological index is a graph invariant that can be utilized to scrutinize the structure and topology of molecules under different conditions. One of such topological indices is the Harmonic index which has received a lot of attention in recent years. In this thesis, we will determine the extremal values of Harmonic index of chemical trees with given number of vertices of maximum degree.