Upper and lower bounds of some graph operations w.r.t. Sombor index

Abstract

A topological index or a connectivity index is a mathematical measure, which is a numerical value that correspond to the chemical structure of a nite graph. Topological indices are isomorphism invariant and is also useful in elds like chemical graph theory, molecular topology and mathematical chemistry. They are an important tool in the study of QSAR (quantitative structure-activity relationships) and QSPR (quantitative structure-property relationships) where chemical structures are associated with other properties of molecules. Recently, due to increasing scope in chemistry, they have become more important. The concept of Sombor index which is a topological index based on degrees, was given by Ivan Gutman in the eld of chemical graph theory. The upper bounds as well as the lower bounds of Sombor index of graphs have been already calculated. In this research work, we computed the upper and lower bounds of some graph operations w.r.t. Sombor index.