Browsing by Author "Yamac, Kerem"

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Modeling Benzene Physicochemical Properties Using Zagreb Upsilon Indices
(De Gruyter Poland Sp Z O O, 2025) Ciftci, Idris; Yamac, Kerem; Denizler, Ismail Hakki
Quantitative structure-property relationship (QSPR) frameworks leverage topological indices to model the physicochemical attributes of molecular structures. In this study, we introduce the concept of upsilon degree and define the Zagreb upsilon indices based on this concept. Our findings demonstrate that the second Zagreb upsilon index exhibits the highest predictive accuracy for the pi-electron energy of benzenes, surpassing existing degree-based topological indices with correlation coefficients exceeding 0.93. This accuracy was measured using statistical correlation analysis, and a direct comparison with the Randi & cacute; and geometric-arithmetic indices further supports the superior performance of the second Zagreb upsilon index. Furthermore, structural sensitivity and abruptness analyses, which assess the stability and variation of an index across different molecular structures, indicate that Zagreb upsilon indices offer superior performance compared to alternative indices. These results suggest that Zagreb upsilon indices have significant potential as a new and effective tool for QSPR research.
A Numerical Scheme for Semilinear Singularly Perturbed Reaction-Diffusion Problems
(Walter de Gruyter Gmbh, 2020) Yamac, Kerem; Erdogan, Fevzi
In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov's type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of epsilon. The proposed method was supported by numerical example.
On Ev-Degree and Ve-Degree Based Topological Properties of the Sierpinski Gasket Fractal
(Yildiz Technical Univ, 2019) Yamac, Kerem; Cancan, Murat
In chemistry, pharmacology, medicine and physics molecular graphs have been used to model molecular substances, networks and fractals. Topological indices have been derived from the molecular graphs of chemical compounds, networks and fractals. Topological indices are important tools to analyze the underlying topology of fractals. Many topological indices have been used to understand and to investigate mathematical properties of fractal models. The Sierpinski gasket fractal is important for the study of fractals. Some physical properties of these type fractals were investigated by some researchers. Also certain topological indices of the Sierpinski gasket fractal have been calculated recently. Ve-degree and Ev-degree concepts have been defined recently in graph theory. Ev-degree and Ve-degree topological indices have been defined by using their corresponding classical degree based topological indices. In this study we calculate ev-degree and ve-degree topological indices for the Sierpinski gasket fractal.
On Some Ve-Degree and Harmonic Molecular Topological Properties of Carborundum
(Koya Univ, 2020) Cancan, Murat; Yamac, Kerem; Tas, Ziyattin; Aldemir, Mehmet Serif
Carborundum, also known as silicon carbide which containing carbon and silicon, is a semiconductor. Molecular topological properties of physical substances are important tools to investigate the underlying topology of these substances. Ev-degree and ve-degree based on the molecular topological indices have been defined as parallel to their corresponding classical degree based topological indices in chemical graph theory. Classical degree based topological properties of carborundum have been investigated recently. As a continuation of these studies, in this study, we compute novel ve-degree harmonic, ve-degree sum-connectivity, ve-degree geometric-arithmetic, and ve-degree atom-bond connectivity, the first and the fifth harmonic molecular topological indices of two carborundum structures.