Mathematical modeling and Revan indices of Dominating David Derived Networks based on edge partitions

Abstract

Chemical graph theory provides powerful mathematical tools for analyzing the structural and physicochemical properties of molecular systems. Among the various degree-based descriptors, the Revan indices have recently emerged as effective topological invariants for studying complex chemical and nanostructured networks. In this paper, we present a detailed mathematical investigation of the first, second, and third Revan indices of dominating David derived networks (DDDNs), a family of networks constructed from the honeycomb lattice through edge subdivision and vertex augmentation. Three variants of DDDNs D₁(t), D₂(t), and D₃(t) are examined using systematic edge partition techniques. For each network, exact closed-form expressions for the Revan indices are derived by leveraging the structural regularities inherent to the networks. The obtained expressions highlight clear distinctions in the topological structure of the three variants, reflecting how edge partitions and degree distributions influence Revan index values. The findings contribute new insights into the mathematical behavior of dominating David derived networks and reinforce their relevance to QSPRs/QSARs modeling, nanostructure design, and theoretical chemistry.