A topological index is a real number derived from the structure of a chemical graph. It is helpful to determine the physicochemical and biological properties of a wide range of drugs, and it better reflects the theoretical properties of organic compounds. This is accomplished using degree‐based topological indices. Vitiligo is a common, acquired skin pigmentation disorder that significantly impacts the quality of life. It frequently embodies a therapeutic challenge, resulting in interest in alternative treatments based on vitamin and herbal supplements. In this article, azathioprine, clobetasol, desonide, hydrocortisone valerate, and other drugs utilized to cure vitiligo have discoursed, and the goal of QSPR revision is to determine the mathematical relationship between properties under investigation (e.g., polarity and enthalpy) and diverse descriptors associated with the drugs’ molecule. The QSPR model will help to predict physical properties. In this study, topological indices (TIs) imposed on said drugs were found to have a good correlation with physicochemical properties in this course. Finally, this work can be helpful to design and synthesize new vitiligo treatments and other disease drugs.

A topological index is a molecular descriptor derived from the molecular structure of a chemical substance. These indices can be used to analyze mathematical values and predict various physical properties of drugs. This article discusses tofacitinib, leflunomide, upadacinib, baricitinib, filgotinib, methotrexate, and other drugs used to treat rheumatoid arthritis, and the goal of the QSPR study is to calculate the relationship between the properties under investigation (e.g., boiling point, polarity, and molar volume) and molecular descriptors. Topological indices (TIs) were imposed on said drugs to calculate the correlation with physicochemical properties in this course.

Eulerian numbers (and ''Alternate Eulerian numbers'') are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to represent permutations that provides some other combinatorial interpretations of these numbers. This representation uses a one-to-one correspondence between permutations and the so-called \emphsubexceedant functions.

A topological index is a real number derived from the structure of a chemical graph. It helps determine the physicochemical and biological properties of a wide range of drugs, and it better reflects the theoretical properties of organic compounds. This is accomplished using degree-based topological indices. We examined some of the physiochemical characteristics of thirteen HIV therapy medications and created a QSPR model utilizing nine of the medication’s topological indices. The melting point, boiling point, flash point, complexity, surface tension, etc., of HIV medicines are closely related according to this QSPR model. This work can help to design and synthesize new HIV treatments and other disease drugs.

A topological index is a real number that is obtained from a chemical graph’s structure. Determining the physiochemical and biological characteristics of a variety of medications is useful since it more accurately represents the theoretical characteristics of organic molecules. This is accomplished using degree-based topological indices. The QSPR research has improved the structural understanding of the physiochemical properties of fungicides. Thirteen fungicides are examined for some of their physiochemical properties, and a QSPR model is built using nine of the drugs’ topological indices. Here, we examine the degree to which the topological indices and physiochemical attributes are connected. To do this, we create networks connecting each of the topological indices to the properties of fungicides and computationally construct topological indices of the drugs mentioned above. According to this QSPR model, the melting point, boiling point, flash point, complexity, surface tension, etc. of fungicides are strongly connected. It was discovered that the topological indices (TIs) applied to the fungicides more accurately represent their theoretical features and show a strong correlation with their physical attributes.

Counting polynomials are closely related to certain features of chemical graphs and provide an elegant means of expressing graph topological invariants. The current paper aims to calculate four polynomials for double benzenoid chains, Sadhana, omega, theta, and Padmakar–Ivan (PI). The edge‐cut method is used to derive analytical closed expressions for these polynomials.