Humaira Ijaz FA23-RMT-049Dr. Maqsood AhmadLHR TP 97922026-01-062025https://repository.cuilahore.edu.pk/handle/123456789/176that offers information about the structural, physical, bioactive, and chemical characteristics of the related chemical compound. It is used in chemical graph theory (CGT), a field of mathematical chemistry. The sigma index being a variant of Zagreb indices is regarded as the model for degree-based indices, highly influential, and thoroughly studied. The square of the difference of all edges of the molecular graph Γ with weights 􀀀 dΓ(x)−dΓ(y) 2 is the sigma index σ(Γ). These TIs are extracted from the structure Γ regarding chemical substance and are instrumental in the QSPR/QSAR analysis. Graph operations are critical to creating novel and sophisticated graphs which are of general or chemical interest. To build a connection with the topological indices of the base graphs, it is relevant to investigate several graph operations. To build a connection with the topological indices of the base graphs, it is relevant to investigate several graph operations. One of the main issues in extremal and CGT is determining the most precise formulations of the lower bound as well as upper bound for the proper TI over a family of graphs. Gutman [MATCH Commun. Math. Comput. Chem, 2018 79] introduced the sigma index, established its properties, and studied the inverse problem. Eliasi and Taeri [Discrete Applied Mathematics, 2009 157] introduced four novel graph operations called F-sum graphs. In this study, we intend to formulate precise formulas and bounds on the sigma index for the class of F-sum graphs. Furthermore, we use our results on a variety of cases to confirm their validity and correctnessenDepartment of MathematicsFA23MathematicsDr. Maqsood AhmadGraph Operationstopological indexmathematical chemistry.QSPR/QSAR analysis.Thesis