The Generalized Inverse Sum Indeg Index of Some Graph Operations

Abstract

The study of networks and graphs carried out by topological measures performs a vital role in securing their hidden topologies. This strategy has been extremely used in biomedicine, cheminformatics and bioinformatics, where computations dependent on graph invariants have been made available to communicate the various challenging tasks. In quantitative structure–activity (QSAR) and quantitative structure–property (QSPR) relationship studies, topological invariants are brought into practical action to associate the biological and physicochemical properties and pharmacological activities of materials and chemical compounds. In these studies, the degree-based topological invariants have found a significant position among the other descriptors due to the ease of their computing process and the speed with which these computations can be performed. Thereby, assessing these invariants is one of the flourishing lines of research. The generalized form of the degree-based inverse sum indeg index has recently been introduced. Many degree-based topological invariants can be derived from the generalized form of this index. In this paper, we provided the bounds related to this index for some graph operations, including the Kronecker product, join, corona product, Cartesian product, disjunction, and symmetric difference. We also presented the exact formula of this index for the disjoint union, linking, and splicing of graphs.

Keywords

• generalized inverse sum indeg index
• graph operations
• vertex degree