On Entropy Measure of Different Families of Fullerenes

Abstract

A topological index is a numerical value assigned to a graph, which represents specific topological properties or characteristics of the graph. It serves as a quantitative measure to analyze and compare the structural features of different graphs. Topological indices have extensive applications in the field of graph theory, enabling the study and understanding of various graph structures and their properties.Topological indices can be categorized based on three main criteria: degree, distance, and spectrum. These categories help organize the different types of indices and provide a framework for analyzing graph structures.Hosoya entropy is a metric in graph theory that quantifies the complexity of a graph’s struc- ture and the connectivity patterns it exhibits. It is computed using the Hosoya polynomial, which counts the number of distinct walks between any pair of vertices in the graph. The resulting Hosoya entropy value provides a numerical representation of the graph’s topolog- ical characteristics and symmetry properties. In this thesis we compute the Hosoya entropy of different fullerene graphs by understanding the structures of fullerenes and compute dis- tance to partition them in Hosoya classes.