Computation of first Zagreb index, second Zagreb index and F-index for subdivision-edge-cycle corona product of graphs

Abstract

In this paper, we introduce a novel graph structure, namely the subdivision-edge-cycle graph, denoted by SE 1 (X), and derive explicit expressions for the first Zagreb index, second Zagreb index and F-index. The chemical relevance of the proposed graph transformation is demonstrated through QSPR modeling of benzenoid hydrocarbons, where it exhibits strong correlations with π-electron energy, molar refractivity, polarizability and exact mass outperforming the corresponding Zagreb indices and F-index of T 1 (X), T 2 (X), and T(X) graphs across linear, quadratic, and cubic regression models. Furthermore, we define a four types of graph operations involving subdivision-edge-cycle graph namely the SE 1 -vertex corona product, SE 1 -edge corona product, SE 1 -vertex neighborhood corona product, and SE 1 -edge neighborhood corona product. For each of these constructions, closed-form expressions for the first Zagreb index, second Zagreb index and F-index are obtained. In addition, bounds for the general sum-connectivity index of these graphs are established.