Computing Some Eccentric Connectivity Indices Based on Vertices and Edges of Backbone DNA Graphs

Graph theory plays a central role in mathematics, biology, chemistry, computer science, and related disciplines. It has many applications in everyday life, particularly in chemistry, biology, and network theory. Chemical graph theory is a subfield devoted to the mathematical representation and analysis of molecular structures. It is also used in the calculation of topological indices and the prediction of many chemical properties. A topological index is a numerical parameter that characterizes the molecular structure based on its corresponding molecular graph. Consider a simple molecular graph G = (V(G), E(G)) with no loops, multiple edges, or directed edges. Numerous topological indices have been defined and studied for molecular graphs. The vertex and edge eccentric connectivity indices, along with their modified versions, play a significant role in QSPR/QSAR studies within the framework of chemical graph theory. Recently, various studies have been conducted on the backbone DNA graphs. The repeating cycles in the backbone DNA graphs indicate that the graph possesses a periodic and regular symmetry. This symmetry is taken into account in deriving closed formulas for topological index values such as the eccentric connectivity indices. In this paper, some eccentric connectivity indices based on vertices and edges of backbone DNA graphs DNA_n have been computed. Furthermore, the two-dimensional plots of DNA_n were generated using Cartesian coordinates.