Özge Çolakoğlu Havare

Predicting physicochemical properties of chemical compounds in a cost-effective and non-experimental manner is of great importance. This is often achieved using topological indices derived from graph theory. Topological index is the numerical value obtained from the structural property of the graph obtained by modeling the chemical structure with graph theory. Bipolar disorder is a mental health condition characterized by mood swings, including manic/hypomanic and depressive episodes. In this study, various Zagreb topological indices based on vertex degree, edge degree, and eccentricity are calculated for graphs of drugs used in the treatment of bipolar disorder. Furthermore, QSPR (quantitative structure property relationship) models are developed to predict the boiling point, enthalpy of vaporization, flash point, molar refractivity and polarizability of these drugs. This study determines the version of the Zagreb indices that best predict the physicochemical properties of bipolar drugs and the corresponding model. The findings demonstrate the potential of using mathematical descriptors in designing and evaluating pharmaceutical compounds.

Molecular descriptors (graph indices) numerically describe the topologies of the chemicals. Graph indices are used to estimate certain properties of molecules. In this paper, reformulated first/second Zagreb indices for the thorny graph of any graph are obtained. Exact results are given for the reformulated Zagreb indices of thorny graphs of some special graphs. Reformulated Zagreb indices of the propyl ether imine (PETIM) dendrimers calculated and these indices are compared numerically. In addition, algorithms are designed to calculate the reformulated first/second Zagreb indices of graphs.

Chemical graph theory is a branch of graph theory. In this field, molecules are modeled using graph theory and a mathematical approach is obtained. Thus, predictions can be made about the physical, chemical and bioactivity properties of molecules. In this study, temperature indices depending on the vertex degree are considered. Temperature indices of Polyamidoamine (PAMAM) dendrimers, Porphyrin core dendrimers are obtained and the results are compared numerically using the MATLAB program.

Graph invariants (topological indices) are numerical values of graphs obtained from 2-dimensional (2-D) images of chemical structures. These invariants are used in the structure-property/activity studies to predict certain properties such as the enthalpy of vaporization, and stability of molecular structures. In this paper, reformulated Zagreb indices, which are edge-degree-based indices, are considered. First, the reformulated Zagreb indices for cycle-related graphs which are wheel, helm, gear, friendship, closed helm, flower, sun, and sunflower are computed. The values of the first and second reformulated Zagreb indices of cycle-related these graphs and also the values of reformulated Zagreb indices of graphs with the same edge cardinality among studied graphs are compared numerically with the MATLAB software program. Finally, reformulated first Zagreb index and reformulated second Zagreb index of linear [n]-phenylenes are calculated and these values are computed numerically.

In chemistry and medical sciences, it is essential to study the chemical, biological, clinical, and therapeutic aspects of pharmaceuticals. To save time and money, mathematical chemistry focuses on topological indices used in quantitative structure-property relationship (QSPR) models to predict the properties of chemical structures. The COVID-19 pandemic is widely recognized as the greatest life-threatening crisis facing modern medicine. Scientists have tested various antiviral drugs available to treat COVID-19 disease, and some have found that they help get rid of this viral infection. Antiviral drugs such as Arbidol, chloroquine, hydroxychloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin are used to treat COVID-19. In this paper, reformulated leap Zagreb indices are introduced. Then, the reformulated leap Zagreb indices, leap eccentric connectivity indices, and reformulated Zagreb connectivity indices of these antiviral drugs are calculated. Curvilinear and multilinear regression models predicting the physicochemical properties of these antiviral drugs in terms of proposed indices are obtained and analyzed. The findings and models of this study will shed light on new drug discoveries for the treatment of COVID-19.

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by a graph. Molecular descriptors are used in QSPR/QSAR modeling to determine a chemical structure’s physical, biological, and chemical properties. The cycle graphs are symmetric graphs for any number vertices. In this paper, recently defined neighborhood degree sum-based molecular descriptors and polynomials are studied. NM-polynomials and molecular descriptors of some cycle-related graphs, which consist of the wheel graph, gear graph, helm graph, flower graph, and friendship graph, are computed and compared.

"Topological indices are the numerical descriptors of a molecular structure obtained via molecular graph G. They are used to predict physicochemical and bioactive properties of the molecules and molecular compounds. In this paper, the Mostar index is studied. It is presented the relationships between the Mostar index and other topological indices. Inequalities about some parameters and also Nordhaus-Gaddum-type results for the Mostar index are also presented."

Monkeypox has recently re‐emerged. Since monkeypox has started to be seen in many countries without an epidemic, studies have started on new drugs used to treat this disease. Drug discovery is a challenging process. To alleviate this process, molecular descriptors used to predict the physical, chemical, and biological properties of chemical structures are studied. Molecular descriptors are numerical values of a chemical structure represented by a graph. In this study, M‐polynomial and neighborhood M‐polynomial molecular descriptors of drugs used and candidates for use in monkeypox are calculated and these descriptors are compared.