University of KashanIranian Journal of Mathematical Chemistry2228-648916220250601Geometric-Quadratic Index from a Mathematical Perspective859211488510.22052/ijmc.2024.255277.1890ENBorisFurtulaFaculty of Science, University of Kragujevac, Kragujevac, SerbiaMert SinanOZDepartment of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa, TurkeyJournal Article20240809The geometric-quadratic index (GQ) was defined in 2021 by V. R. Kulli. In a recent study, QSPR analysis for the octane isomers of GQ and some other newly defined topological indices was presented. This analysis has revealed that GQ dominates over many of the well-known topological indices in terms of chemical applicability potential, especially for the heat of vaporization. These results inspired us to investigate the mathematical properties of GQ. In this paper, extremal graphs for GQ are investigated among connected graphs, trees, and unicyclic graphs. In addition, several mathematical relations between GQ and some well-known topological indices are presented.https://ijmc.kashanu.ac.ir/article_114885_8fe670635ed6607eb8ccbcbcd8d9a0f9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648916220250601Harmonic-Arithmetic Index of Unicyclic Graphs9310811488610.22052/ijmc.2024.255486.1909ENGuoqingDingSchool of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, ChinaLingpingZhongSchool of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, ChinaXiaWangSchool of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, ChinaJournal Article20240921Let G=(V(G),E(G)) be a graph. The harmonic-arithmetic index of G is defined as $HA(G)=\sum_{uv\in E(G)}\frac{4d_{G}(u)d_{G}(v)}{(d_{G}(u)+d_{G}(v))^2}$, where $d_{G}(u)$ is the degree of a vertex $u\in V(G)$. In this paper, we consider the upper and lower bounds of the harmonic-arithmetic index of unicyclic graphs with a fixed order. Furthermore, the graphs attaining the extremal values are also characterised.https://ijmc.kashanu.ac.ir/article_114886_f37799c5637364dfbf3464af7fce25a5.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648916220250601Topological Properties of Commuting Graphs over Semi-Dihedral Groups10912611490510.22052/ijmc.2024.254494.1840ENFawadAliCollege of Mathematical Sciences and Statistics, Baise University, Guangxi, Baise 533000, China\\
Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 455505 PakistanKumailRazaInstitute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, KPK, PakistanTanzeelaRubabInstitute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, KPK, PakistanJournal Article20240301The algebraic value of a chemical composition plays a crucial role in determining its physical properties, chemical reactivity, and biological activity. Algebraic graph theory investigates the connection between abstract algebra and graph theory. Focusing on the commuting graphs of semi-dihedral groups, we examine their various topological properties.<br />Furthermore, we provide a detailed exploration of key topological graph indices, including the general Randi\'{c} index, the Wiener index, the atom-bond connectivity index (and its fourth variation), the Schultz molecular topological index, the geometric-arithmetic index, the harmonic index, and the Harary index. This research reveals the structural as well as mathematical features of these graphs, providing valuable insights into their possible applications. https://ijmc.kashanu.ac.ir/article_114905_36cf19ed65cfcb8f1cf9d26bbea1dfcc.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648916220250601Numerical Study of One-Phase Stefan-Type Problems12713911490710.22052/ijmc.2025.255182.1881ENSeyed ShojaeddinPishnamaz MohammadiDepartment of Applied Mathematics, University of Tabriz, IranKarimIvazDepartment of Applied Mathematics, University of Tabriz, IranJournal Article20240822We all know that parabolic equations with non-classical boundary conditions and Stefan's problem have become very popular in recent years due to their many applications in more basic and applied science problems. Also, differential equations with integral conditions have found wide applications in solving chemistry and physics problems. Many problems that appear in heat transfer can be reduced to non-classical problems with integral conditions.<br />In this document, we first mention the application of Stefan's one-phase problems, including the non-classical thermal equation and the integral boundary condition, in problems related to chemistry. Then we examine a numerical technique to solve it and prove the convergence of the method.<br />Finally, numerical examples are presented to demonstrate the effectiveness of the method for solving linear and nonlinear diffusion-response equations with these non-classical conditions.https://ijmc.kashanu.ac.ir/article_114907_284d61138c6bd55abbf4acacc67cd7c3.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648916220250601On Extremal General Multiplicative Zagreb Indices14115311491110.22052/ijmc.2025.255619.1918ENYetneberk KumaFeyissaDepartment of Mathematics, Wolkite University, EthiopiaYohannes GebruAemroDepartment of Mathematics, Wolkite University, EthiopiaHabtamu TsegayeTeferiDepartment of Mathematics, Wolkite University, EthiopiaJournal Article20241020The first general multiplicative Zagreb index $P_1^a(G)$ is the product of the degree of each vertex $v$ in $G$, raised to the power $a$ and the second general multiplicative Zagreb index $P_2^a(G)$ is the product of the degree of each vertex $v$ in $G$, raised to the power $a$ times the degree of $v$, where $a$ is a non-zero real number.<br />In this study, we present bounds on the general multiplicative Zagreb indices for trees and unicyclic graphs. We also provide bounds for the first general multiplicative Zagreb index for trees.<br />Additionally, we identify all the extremal graphs for each bound mentioned as best as possible.https://ijmc.kashanu.ac.ir/article_114911_79473c2d9d910a2aa4cd3c08867346e6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648916220250601A Note on the Additively Weighted Mostar Index of Graphs15517011491210.22052/ijmc.2024.255424.1899ENLijuAlexBishop Chulaparambil Memorial College, Kottayam-686001, IndiaGopalapillaiIndulalDepartment of Mathematics, St.Aloysius College, Edathua, Alappuzha -689573, IndiaJoyamol TBabyBishop Chulaparambil Memorial College, Kottayam-686001, IndiaJournal Article20240908In this article, we discuss the additively weighted Mostar index, an innovative topological measure that extends the traditional Mostar index by incorporating edge weights computed as the sum of the degrees of their end point vertices. We focus on its application within the set $\mathcal{U}_n$ comprising all unicyclic graphs of order $n$. Our study rigorously establishes the first two sharp lower and upper bounds for this index across graphs in $\mathcal{U}_n$. Additionally, we analyze the additively weighted Mostar index of Cartesian product graphs and investigate its properties across various graph classes. Furthermore, we demonstrate the practical utility of this index by comparing its effectiveness against eight other distance-based topological indices in predicting chemical properties of octane isomers. Remarkably, we find that the additively weighted Mostar index outperforms or matches the predictive capabilities of other indices in linear models with these chemical properties, highlighting its potential in quantitative structure-property relationships. This research significantly contributes to both graph theory and chemical informatics by showcasing the unique advantages of the additively weighted Mostar index in structural analysis and predictive modeling.https://ijmc.kashanu.ac.ir/article_114912_dfcd53d40bd7d6b7b75c56502fa209f1.pdf