Bounds on Second Hyper Zagreb Index for Four Graph Operations

Abstract

In the field of chemical graph theory, a Topological index is a numerical value obtained through a mathematical formula involving vertex degrees, distance, spectrum, and their combination. These values are extracted from the molecular graph of a chemical com- pound and are instrumental in the QSPR/QSAR analysis. Operations on the graphs enables us to construct new and valuable molecular graphs of future chemical compounds. A fas- cinating area of inquiry in chemical graph theory is determining the closed form formulas and bounds of relevant topological indices within a specific family of graphs. Our project focuses on computing the exact formulas of the Y-index for F-sum related to tensor product, and we have included various examples to verify our findings.