Abstract:
Graph theory acts as an essential tool in various fields and applications because of its
versatility in modeling and solving problems involving relationships and connections.
In this thesis, our aim is to compute the eccentricity based topological indices like to-
tal eccentricity, Zagreb indices, average eccentricity, Geometric Arithmetic index GA,
atom-bond connectivity ABC index for the line graphs of first type of Hex-Derived
Networks HDN1(s) as well as some other chemical structures. Furthermore, the basic
topologies of these networks are also derived. We obtained their respective indices
based on the categorization of the chemical graphs. These newly obtained indices give
insight into the chemical and physical properties of molecules. This analysis will assist
researchers engaged in the field of network sciences by clarifying the structure of the
aforementioned networks. Moreover, the results presented in this thesis might offer ad-
vantages in predicting supplementary chemical, physical and structural characteristics
of the molecular graphs being studied.
