University of KashanIranian Journal of Mathematical Chemistry2228-648917320260901Concentration of Ethanol and Acetaldehyde Inside the Catalyst Particle and in the Reaction Stream: Theoretical and Numerical Approach23325311571810.22052/ijmc.2026.257981.2091ENBaskaranYamunaDepartment of Mathematics, Saraswathi Narayanan College, Madurai-625022, India0009-0008-6562-4427AthimoolamMeenaDepartment of Mathematics, Saraswathi Narayanan College, Madurai-625022, India0000-0003-2312-6848LakshmananRajendranDepartment of Mathematics, AMET Deemed to be University, Kanathur, Chennai- 603112, India0000-0002-2003-4553MohammadIzadiDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran,\\Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India0000-0002-6116-4928Journal Article20251117The current research investigates the nonlinear behaviour of dimensionless ethanol and acetaldehyde concentrations in a fixed-bed laboratory reactor operating with a ${Mn}_9{Cu}_1$ catalyst for catalytic combustion. The main objective is to obtain accurate analytical solutions of the coupled nonlinear governing equations and evaluate their usefulness for reactor analysis. A semi-analytical hyperbolic function method is applied to derive rapidly convergent solutions, which are validated through MATLAB (version 7.8.0, R2009a) numerical simulations. Excellent agreement between analytical and numerical results confirms the reliability of the method. The findings show that the approach efficiently captures reactive transport and catalytic kinetics while reducing computational iteration time. The solutions provide insight into catalyst performance and ethanol oxidation efficiency, supporting optimization of reactor operating conditions. Overall, the study demonstrates that the hyperbolic function method is a simple, computationally efficient tool for modelling complex nonlinear catalytic combustion systems.https://ijmc.kashanu.ac.ir/article_115718_ca517f33fc250e5d8a31665ac2915c89.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917320260901Comment on "Lower and Upper Bounds between Energy, Laplacian Energy, and Sombor Index of Some Graphs" [Iranian J. Math. Chem. 16 (2025) 33-38]25525711571910.22052/ijmc.2026.259092.2166ENXiaoyeDingCollege of Big Data and Artificial Intelligence, Anhui Xinhua University, Hefei, 230088, China0000-0001-5318-3507XuewuZuoCollege of Big Data and Artificial Intelligence, Anhui Xinhua University, Hefei, 230088, ChinaMuratCancanFaculty of Education, Van Yuzuncu Yil University, Van, TurkeyJournal Article20260628This note corrects several errors in the published paper (Barzegar, 2025). We identify the main flaws and present corrected versions of the affected results.https://ijmc.kashanu.ac.ir/article_115719_017cbe61413e59cdc7370d4017bd3d91.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917320260901Extremal Results and Inequalities for the Diminished Sombor Index of Graphs25927011572910.22052/ijmc.2026.258144.2101ENMohammad HadiAkhbariDepartment of Mathematics, Es.C., Islamic Azad University, Estahban, Iran0000-0002-2669-4966FatemeMovahediDepartment of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran0000-0001-7863-7915Journal Article20251216For any simple graph \(G \) having an edge set \(E\), the Diminished Sombor index (DSO) is formulated as: <br>DSO(G)= \sum_{uv \in E} \frac{\sqrt{\zeta_u^2 + \zeta_v^2}}{\zeta_u + \zeta_v},<br>where \(\zeta_u\) is the degree of the vertex u.<br>The present paper focuses on the DSO index of simple graphs, where precise bounds are derived based on fundamental structural parameters, including order, size, maximum degree, and minimum degree. We also establish sharp inequalities relating DSO to a collection of standard topological indices, namely the Randi\'c, Geometric-Arithmetic, Zagreb, Sombor, and Harmonic indices, as well as inverse degree-related indices. For each bound, extremal graphs attaining equality are fully characterized. Additionally, we analyze the behavior of DSO for specific graph families, including trees and regular graphs.https://ijmc.kashanu.ac.ir/article_115729_c5c2a991d92b4f9244c12c38238fbbb6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917320260901A Note on the General Gutman Index of Graphs27128511573510.22052/ijmc.2025.257853.2079ENZohrehJamalkashaniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IranGholam HosseinFath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0003-1105-3020MahdiSabzevariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IranJournal Article20251027The general Gutman index, denoted by $G_{a,b}(H)$, is a prominent distance–degree-based topological index in chemical graph theory, defined using a combination of vertex degrees and intervertex distances. In this paper, we focus on bicyclic graphs as a special class of graphs and investigate the behavior of this index within that setting. In particular, we examine the case $G_{2,1}(H)$. The primary objective of this study is to establish a sharp upper bound for the general Gutman index in bicyclic graphs. By exploiting the structural properties of bicyclic graphs and employing combinatorial techniques, we derive a sharp upper bound for this index. The results obtained may provide a useful foundation for further research on distance-degree-based indices and their structural implications in mathematical chemistry.https://ijmc.kashanu.ac.ir/article_115735_a99546f93372387485650d3aff7fc09a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917320260901Kirchhoff, Multiplicative and Additive Degree-Kirchhoff Indices in Random Cyclodecane Chains28730611573610.22052/ijmc.2026.257678.2073ENXuanJiangDepartment of Data Science, Anhui University of Technology , Maanshan, 243032, Anhui, ChinaPingpingChenSchool of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, ChinaKaiZhouSchool of Big Data and Artificial Intelligence, Center of Applied Mathematics, Chizhou University, Chizhou, 247000, Anhui, ChinaDuoduoZhaoSchool of Big Data and Artificial Intelligence, Center of Applied Mathematics, Chizhou University, Chizhou, 247000, Anhui, China0009-0003-0667-0478Journal Article20250929The Kirchhoff index serves as a significant measure in characterizing molecular topological structures. It quantifies atomic connectivity within molecules and facilitates the correlation and prediction of physicochemical properties and biological activities of chemical compounds, thereby holding considerable practical value. This paper derives recurrence relations for the expected values of three variants of the Kirchhoff index, the multiplicative degree-Kirchhoff index, and the additive degree-Kirchhoff index in random cyclodecane chains using a recursive approach. Based on these relations, the extremal values and average values of these indices are obtained for a cyclodecane chain composed of $n$ regular decagons. Furthermore, it is shown that the expected Kirchhoff indices of the random cyclodecane chain equal the average of the corresponding indices over five specific structural configurations of the chain.https://ijmc.kashanu.ac.ir/article_115736_35072f52eb0bc3efb2b1f5ca8cc2d822.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917320260901Vertex-Degree-Based Energy for Selected Classes of Molecular Graphs30732811575710.22052/ijmc.2026.258159.2105ENAlmasaOdzakDepartment of Mathematics and Computer Science, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina0000-0001-6269-9759LamijaŠćetaSchool of Economics and Business, University of Sarajevo, Trg Oslobodjenja Alija Izetbegovi\'{c} 1, 71 000 Sarajevo, Bosnia and Herzegovina0000-0002-0410-0311MedinaZubacaDepartment of Mathematics and Computer Science, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina0000-0001-9669-3312Journal Article20251218Vertex-degree-based matrices and their corresponding energies provide a unified framework that encompasses many matrices and energies induced by classical vertex-degree-based topological indices. This framework is motivated by the correlation between these indices and the structural and energetic properties of chemical compounds. Closed-form expressions for the energies induced by vertex-degree-based functions of a highly general four-parameter form are derived for several representative classes of graphs, including some graph products. This offers new insights into the spectral behaviour of molecular structures and expands the applicability of vertex-degree-based descriptors to a broader range of chemical and network systems, as well as QSAR/QSPR modelling.https://ijmc.kashanu.ac.ir/article_115757_838eb2257189336330b064b3b3459692.pdf