Tuberculosis (TB) is one of the most contagious diseases that has a greater mortality rate than HIV/AIDS and the cases of TB are feared to rise as a repercussion of the COVID-19 pandemic. The pharmaceutical industry is constantly looking for ways to improve drug design processes in order to combat the growth of infections and cure newly identified syndromes or genetically based dysfunctions with the help of QSPR models. QSPR models are mathematical tools that establish relationships between a molecular structure and its physicochemical attributes using structural properties. Topological indices are such properties that are generated from the molecular graph without any empirically derived measurements. This work focuses on developing a QSPR model using distance-based topological indices for anti-tuberculosis medications and their diverse physicochemical features.

Entropy is a thermodynamic function used in chemistry to determine the disorder and irregularities of molecules in a specific system or process. It does this by calculating the possible configurations for each molecule. It is applicable to numerous issues in biology, inorganic and organic chemistry, and other relevant fields. Metal–organic frameworks (MOFs) are a family of molecules that have piqued the curiosity of scientists in recent years. They are extensively researched due to their prospective applications and the increasing amount of information about them. Scientists are constantly discovering novel MOFs, which results in an increasing number of representations every year. Furthermore, new applications for MOFs continue to arise, illustrating the materials’ adaptability. This article investigates the characterisation of the metal–organic framework of iron(III) tetra-p-tolyl porphyrin (FeTPyP) and CoBHT (CO) lattice. By constructing these structures with degree-based indices such as the K-Banhatti, redefined Zagreb, and the atom-bond sum connectivity indices, we also employ the information function to compute entropies.

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.

Due to significant advancements being made in the field of drug design, the use of topological descriptors remains the primary approach. When combined with QSPR models, descriptors illustrate a molecule’s chemical properties numerically. Numbers relating to chemical composition topological indices are structures that link chemical composition to physical characteristics. This research concentrates on the analysis of curvilinear regression models and degree-based topological descriptors for thirteen skin cancer drugs. The physicochemical characteristics of the skin cancer drugs are examined while regression models are built for computed index values. An analysis is performed for several significant results based on the acquired data.

Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. We explain the basic applications of distance-based entropy to chemical phenomena. These applications include signal processing, structural studies on crystals, molecular ensembles, and quantifying the chemical and electrical structures of molecules. In this study, we examine the characterisation of polyphenylenes and boron ($B_{12}$) using a line of symmetry. Our ability to quickly ascertain the valences of each atom, and the total number of atom bonds is made possible by the symmetrical chemical structures of polyphenylenes and boron $B_{12}$. By constructing these structures with degree-based indices, namely the K Banhatti indices, $ReZ{G}_1$-index, $ReZ{G}_2$-index, and $ReZ{G}_3$-index, we are able to determine their respective entropies.

A topological index, which is a number, is connected to a graph. It is often used in chemometrics, biomedicine, and bioinformatics to anticipate various physicochemical properties and biological activities of compounds. The purpose of this article is to encourage original research focused on topological graph indices for the drugs azacitidine, decitabine, and guadecitabine as well as an investigation of the genesis of symmetry in actual networks. Symmetry is a universal phenomenon that applies nature’s conservation rules to complicated systems. Although symmetry is a ubiquitous structural characteristic of complex networks, it has only been seldom examined in real-world networks. The $\overline{M}$-polynomial, one of these polynomials, is used to create a number of degree-based topological coindices. Patients with higher-risk myelodysplastic syndromes, chronic myelomonocytic leukemia, and acute myeloid leukemia who are not candidates for intense regimens, such as induction chemotherapy, are treated with these hypomethylating drugs. Examples of these drugs are decitabine (5-aza-20-deoxycytidine), guadecitabine, and azacitidine. The $\overline{M}$-polynomial is used in this study to construct a variety of coindices for the three brief medicines that are suggested. New cancer therapies could be developed using indice knowledge, specifically the first Zagreb index, second Zagreb index, F-index, reformulated Zagreb index, modified Zagreb, symmetric division index, inverse sum index, harmonic index, and augmented Zagreb index for the drugs azacitidine, decitabine, and guadecitabine.