University of KashanIranian Journal of Mathematical Chemistry2228-648914420231201Lower Bounds on the Entire Sombor Index19520511410010.22052/ijmc.2023.253281.1739ENNasrinDehgardiDepartment of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, IranJournal Article20230719Let $G=(V,E)$ be a graph. The entire Sombor index of graph $G$, $ SO^\varepsilon(G) $ is defined as the sum of the terms<br />$\sqrt{d_{G}^2(a)+d_{G}^2(b)}$, where $a$ is either adjacent to or incident with $b$ and<br />$a,b\in V\cup E$.<br />It is known that if $T$ is a tree of order $n$, then $SO^\varepsilon(T)\ge 6\sqrt{5}+8(n-3)\sqrt{2}$. We improve this result and establish best lower bounds on the entire Sombor index with given vertices number and maximum degree. Also, we determine the extremal trees achieve these bounds.https://ijmc.kashanu.ac.ir/article_114100_0165f87626c23140ed11b5b6803ea920.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914420231201Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique for Time-Fractional KdV-Burgers' Equation20722411410210.22052/ijmc.2023.252824.1710ENAhmed GamalAttaDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, EgyptYoussriHassan YoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptJournal Article20230418The main goal of this research work is to provide a numerical technique based on choosing a set of basis functions for handling the third-order time-fractional Korteweg–De Vries Burgers' equation. The trial functions are selected for the shifted second-kind Chebyshev polynomials (S2KCPs) compatible with the problem's governing initial and boundary conditions. The spectral tau method transforms the equation and its underlying conditions into a nonlinear system of algebraic equations that can be efficiently numerically inverted with the standard Newton's iterative procedures after the approximate solutions have been expressed as a double expansion of the two chosen basis functions. The truncation error is estimated. Various numerical examples are displayed together with comparisons to other approaches in the literature to show the applicability and accuracy of the provided methodology. Different numerical models are displayed and compared to other methods in the literature.https://ijmc.kashanu.ac.ir/article_114102_4f98190a4c99d232347d42467073fe23.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914420231201Quantization of Sombor Energy for Complete Graphs with Self-Loops of Large Size22524111411610.22052/ijmc.2023.252770.1707ENJohnnyLimSchool of Mathematical Sciences, Universiti Sains Malaysia, MalaysiaZheng KiatChewSchool of Mathematical Sciences, Universiti Sains Malaysia, MalaysiaMacco Zhi PeiLimSchool of Mathematical Sciences, Universiti Sains Malaysia, MalaysiaKai JieThooSchool of Mathematical Sciences, Universiti Sains Malaysia, MalaysiaJournal Article20230408A self-loop graph $G_S$ is a simple graph $G$ obtained by attaching loops at $S \subseteq V(G).$ To such $G_S$ an Euclidean metric function is assigned to its vertices, forming the so-called Sombor matrix. In this paper, we derive two summation formulas for the spectrum of the Sombor matrix associated with $G_S,$ for which a Forgotten-like index arises. We explicitly study the Sombor energy $\cE_{SO}$ of complete graphs with self-loops $(K_n)_S,$ as the sum of the absolute value of the difference of its Sombor eigenvalues and an averaged trace. The behavior of this energy and its change for a large number of vertices $n$ and loops $\sigma$ is then studied. Surprisingly, the constant $4\sqrt{2}$ is obtained repeatedly in several scenarios, yielding a quantization of the energy change of 1 loop for large $n$ and $\sigma$.<br />Finally, we provide a McClelland-type and determinantal-type upper and lower bounds for $\cE_{SO}(G_S),$ which generalizes several bounds in the literature.https://ijmc.kashanu.ac.ir/article_114116_27abc540d655033b358779bc2dd1c63d.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914420231201The Effect of Fractional-Order Derivative for Pattern Formation of Brusselator Reaction–Diffusion Model Occurring in Chemical Reactions24326911411810.22052/ijmc.2023.253498.1759ENMostafaAbbaszadehDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University
of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, IranAlirezaBagheri SalecDepartment of Mathematics, Faculty of Basic Scince, University of Qom Alghadir Blvd., Qom, IranShurooq KamelAbd Al-KhafajiDepartment of Mathematics, Faculty of Basic Scince, University of Qom Alghadir Blvd., Qom, IranJournal Article20230828The space fractional PDEs (SFPDEs) have attracted a lot of attention. Developing high-order and stable numerical algorithms for them is the main aim of most researchers. This research work presents a fractional spectral collocation method to solve the fractional models with space fractional derivative which is defined based upon the Riesz derivative. First, a second-order difference formulation is used to approximate the time derivative. The stability property and convergence order of the semi-discrete scheme are analyzed. Then, the fractional spectral collocation method based on the fractional Jacobi polynomials is employed to discrete the spatial variable. In the numerical results, the effect of fractional order is studied.https://ijmc.kashanu.ac.ir/article_114118_a6f2e0980c602cda4a2ce4eff53165c6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914420231201On Nirmala Indices-based Entropy Measures of Silicon Carbide Network27128811412210.22052/ijmc.2023.252742.1704ENVirendraKumarDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh,
India.ShibsankarDasDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh,
India.0000-0003-0082-6673Journal Article20230331Topological indices are numerical parameters for understanding the fundamental topology of chemical structures that correlate with the quantitative structure-property relationship (QSPR) / quantitative structure-activity relationship (QSAR) of chemical compounds. The M-polynomial is a modern mathematical approach to finding the degree-based topological indices of molecular graphs.<br />Several graph assets have been employed to discriminate the construction of entropy measures from the molecular graph of a chemical compound. Graph entropies have evolved as information-theoretic tools to investigate the structural information of a molecular graph. The possible applications of graph entropy measures in chemistry, biology and discrete mathematics have drawn the attention of researchers. In this research work, we compute the Nirmala index, first and second inverse Nirmala index for silicon carbide network $Si_{2}C_{3}\textit{-I}[p,q]$ with the help of its M-polynomial. Further, we introduce the concept of Nirmala indices-based entropy measure and enumerate them for the above-said network. Additionally, the comparison and correlation between the Nirmala indices and their associated entropy measures are presented through numerical computation and graphical approaches. Following that, curve fitting and correlation analysis are performed to investigate the relationship between the Nirmala indices and corresponding entropy measures.https://ijmc.kashanu.ac.ir/article_114122_39babab03dc25311ca588ab304fe4c89.pdf