Computation of degree-based topological indices for the complex structure of ruthenium bipyridine

In graph theory, a topological index is an important descriptor that helps analyze the physicochemical properties of the structure of chemical compounds through a chemical graph. Degree-based topological indices have been extensively studied and linked to a variety of chemical properties. This work aims to construct a complex ruthenium-bipyridine polymer structure involving triphenylamine, which will be useful in the manufacture of organic light-emitting diodes, solar cells, organic field-effect transistors, and photorefractive materials, especially as hole transport material. In order to study this novel complex ruthenium bipyridine structure, we employ a reliable mathematical tool called M-polynomial and NM-polynomial of the topological index, which displays some physical and chemical properties in numerical form. Due to ruthenium's ability to exist in a variety of oxidation states and its simple ability to interact with ligands, a variety of molecular structures can be easily created for a ruthenium core. We developed the complex structure of ruthenium bipyridine, which is composed of a metal (ruthenium) and an organic ligand (triphenylamine).image