Cancer is a deadly disease. There is no drug yet for the treatment of some types of cancer. New drug trials are being conducted to treat this disease. One of them is HDAC‐based multi‐target drugs. Topological indices (TIs) are the numerical descriptors of a molecular structure obtained by the molecular graph. TIs can be used in the structure–property relationship (QSPR) and structure–activity relationship studies to provide information about the physicochemical properties and biological properties of molecules. In this paper, vorinostat, tucidinostat, triciferol, and CUDC‐101 and CUDC‐907, which are seen as an important light in cancer treatment, are studied. M‐polynomials based on degree and NM‐polynomials based on the sum of degrees of neighboring vertices for chemical graphs of these drugs are calculated. By using these polynomials, many TIs that depend on the degree and the sum of neighboring degrees are obtained. Moreover, The QSPR models are designed using these TIs to estimate some physicochemical properties of these drugs. The QSPR studies are obtained using the curvilinear regression method.

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In the present work the -adic gamma function has been considered. The Volkenborn integral of the -adic gamma function by using its Mahler expansion has been derived. Moreover, a new representation for the -adic Euler constant has been given.

COVID-19, which has spread all over the world and was declared as a pandemic, is a new disease caused by the coronavirus family. There is no medicine yet to prevent or end this pandemic. Even if existing drugs are used to alleviate the pandemic, this is not enough. Therefore, combinations of existing drugs and their analogs are being studied. Vaccines produced for COVID-19 may not be effective for new variants of this virus. Therefore, it is necessary to find the drugs for this disease as soon as possible. Topological indices are the numerical descriptors of a molecular structure obtained by the molecular graph. 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 paper, some analogs of lopinavir, favipiravir, and ritonavir drugs that have the property of being potential drugs against COVID-19 are studied. QSPR models are studied using linear and quadratic regression analysis with topological indices for enthalpy of vaporization, flash point, molar refractivity, polarizability, surface tension, and molar volume properties of these analogs.

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