Some Degree-Based Topological Indices Associated With Line Graphs of Backbone Deoxyribonucleic Acid Networks: A Polynomial Function Approximation

Topological indices have applications in understanding the structural characteristics of molecular networks, especially in computational chemistry and bioinformatics. In this research, we explore the degree-based topological indices associated with the line graphs of the backbone deoxyribonucleic acid network, denoted by DNAn, and segmented backbone deoxyribonucleic acid network, denoted by SDNAn, using the direct method and present polynomial approximations that can forecast their behavior. By polynomial approaches, we obtain mathematical representations that are exceptionally compatible with several topological indices, including the degree-based Banhatti and Sombor indices. The suggested polynomial models give a computationally effective alternative for calculating these indices, providing information on the structural complexity of backbone deoxyribonucleic acid and segmented backbone deoxyribonucleic acid networks. The findings demonstrate the efficacy of polynomial-based techniques in identifying these networks on a wide scale, with possible chemical and networking applications.