On the indices of certain graph products

Abstract

Molecular descriptors are numerical graph invariants that are used to study the chemical structure of molecules. In this paper, we determine the upper bound of the Sombor index based on four operations involving the subdivision graph, semi-total point graph, semi-total line graph, and total graph related to the lexicographic and tensor product. The exact expressions of the first reformulated Zagreb index and the second hyper-Zagreb index of the tensor product are formulated on the basis of the four significant graphs. Further, the descriptors for certain standard graphs are obtained and the graphical comparison for the first reformulated Zagreb index has also been illustrated to understand the result better.

Keywords

• sombor index
• lexicographic product
• tensor product