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.

Based on topological descriptors, QSPR analysis is an incredibly helpful statistical method for examining many physical and chemical properties of compounds without demanding costly and time-consuming laboratory tests. Firstly, we discuss and provide research on kidney cancer drugs using topological indices and done partition of the edges of kidney cancer drugs which are based on the degree. Secondly, we examine the attributes of nineteen drugs casodex, eligard, mitoxanrone, rubraca, and zoladex, etc and among others, using linear QSPR model. The study in the article not only demonstrates a good correlation between TIs and physical characteristics with the QSPR model being the most suitable for predicting complexity, enthalpy, molar refractivity, and other factors and a best-fit model is attained in this study. This theoretical approach might benefit chemists and professionals in the pharmaceutical industry to forecast the characteristics of kidney cancer therapies. This leads towards new opportunities to paved the way for drug discovery and the formation of efficient and suitable treatment options in therapeutic targeting. We also employed multicriteria decision making techniques like COPRAS and PROMETHEE-II for ranking of said disease treatment drugs and physicochemical characteristics.