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.
