In quantitative structure property (QSPR) and quantitative structure activity (QSAR) relationships studies, topological indices are utilized to associate the biological activity of underline structures with their physical properties like strain energy, distortion, melting point, boiling point, and stability, etc. In these studies, the degree based topological indices have obtained center position between various kind of descriptors, due to the simplicity of finding and the rapidity with which these estimations can be accomplished. In this paper, we compute the general Randic, first and second Zagreb, Atom Bond Connectivity(ABC) and Geometric Arithmetic(GA) indices of the $2D$ structures of trans-$\mathit{Pd}-({\mathit{NH}}_2)S$ lattice and a metal–organic superlattice. Furthermore, we present the precise formulas of the fifth version of Geometric Arithmetic index and the fourth version of Atom-Bond Connectivity index of these lattices.

Topological indices are numerical numbers that represent the topology of a molecule and are calculated from the graphical depiction of the molecule. The importance of topological indices is due to their use as descriptors in QSPR/QSAR modeling. QSPRs (quantitative structure-property relationships) and QSARs (quantitative structure-activity relationships) are mathematical correlations between a specified molecular property or biological activity and one or more physicochemical and/or molecular structural properties. In this paper, we give explicit expressions of some degree-based topological indices of two classes of metal-organic frameworks (MOFs), namely, butylated hydroxytoluene- (BHT-) based metal-organic ( $\text{M}=\text{Co}$ , Fe, Mn, Cr) (MBHT) frameworks and ${\text{M}}_1\text{TPyP}-{\text{M}}_2$ (TPyP = $\mathrm{5,10,15,20}$ -tetrakis(4-pyridyl)porphyrin and ${\text{M}}_1,{\text{M}}_2$ = Fe and Co) MOFs.

Topological indices are numerical numbers assigned to molecular graphs and are expected to predict certain of its physical or chemical properties. Metal-organic frameworks (MOFs) are inorganic/organic porous crystalline materials with a regular array of positively charged metal ions which surrounds organic linkers. Covalent organic frameworks (COFs) are a class of organic polymers with highly ordered structure and permanent porosity. In this work, we have computed some degree-based topological indices of naphthalene metal-organic frameworks and thiophene-based covalent triazine framework.

People around the world have been suffering from anxiety for a long time. This disease affects about millions people worldwide each year. Antianxiety drugs are used to treat this disease.These antianxiety drugs are available in various forms including antidepressants, benzodiazepines, anticonvulsants, antihistamines, and azaperone. Topological indices can provide information about the physicochemical properties and biological properties of molecules in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this proposed work, various topological indices are defined on some 3D molecular graphs of antianxiety drugs to help the researchers to know the physical characteristics and chemical reaction associated with them. We also discuss the QSPR analysis of twelve degree based topological indices. Furthermore, we calculate the fifth version of geometric arithmetic index and the fourth version of atom-bond connectivity index of 3D graphs. QSPR models are studied using linear regression analysis with topological indices for melting point, boiling point, enthalpy of vaporization, flash point, molar refractivity, polarizability, surface tension, and molar volume properties of these analogs.

In the fields of mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are an analytical framework of a graph which portray its topology and are mostly equal graphs. Topological indices (TIs) are numeral quantities that are used to foresee the natural correlation among the physicochemical properties of the chemical compounds in their fundamental network. TIs show an essential role in the theoretical abstract and environmental chemistry and pharmacology. In this paper, we compute many latest developed degree-based TIs. An analogy among the computed different versions of the TIs with the help of the numerical values and their graphs is also included .In this article, we compute the first Zagreb index, second Zagreb index, hyper Zagreb index, ABC Index, GA Index, and first Zagreb polynomial and second Zagreb polynomial of chemical graphs polythiophene, nylon 6,6, and the backbone structure of DNA.

To connect the biological activity of quantitative structure - activity (QSAR) and quantitative structure - property (QSPR) interactions, topological indices ar...