Bounds on Second Hyper Zagreb Index for Four Graph Operations

Abstract

In the field of chemical graph theory, a molecular descriptor 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 compound 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 fascinating area of inquiry in chemical graph theory is determining the upper and lower limits of relevant topological indices within a specific family of graphs. Our project focuses on computing the bounds of the second hyper Zagreb index for four graph operations, and we have included various examples to verify our findings.