University of KashanIranian Journal of Mathematical Chemistry2228-648915420241201On the Reduced and Increased Sombor Indices of Trees with Given Order and Maximum Degree22723711454910.22052/ijmc.2024.254548.1845ENNasrinDehgardiDepartment of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, IranMahdiehAzariDepartment of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran0000-0002-0919-0598Journal Article20240313The Sombor index is a newly introduced vertex-degree-based graph invariant with the ability to predict the enthalpy<br />of vaporization and entropy of octane isomers. Recently, two new variants of the Sombor index namely the reduced and increased Sombor indices were put forward. The reduced and increased Sombor indices are respectively defined for graph $\Gamma$ as<br />$$SO_{red}(\Gamma)=\sum_{\mathcal{FG}\inE(\Gamma)}\sqrt{(d_{\Gamma}(\mathcal{F})-1)^2+(d_{\Gamma}(\mathcal{G})-1)^2},$$<br /> and<br />$$SO^{\ddagger}(\Gamma)=\sum_{\mathcal{FG}\inE({\Gamma})}\sqrt{(d_{\Gamma}(\mathcal{F})+1)^2+(d_{\Gamma}(\mathcal{G})+1)^2},$$<br /> in which $d_{\Gamma}(\mathcal{F})$ is the degree of the vertex $\mathcal{F}$ in $\Gamma$.<br /> Our purpose is to establish sharp lower bounds on the reduced and increased Sombor indices of trees in terms of their order and maximum vertex degree. Moreover, the extremal trees that attain the bounds are characterized.https://ijmc.kashanu.ac.ir/article_114549_2d296199b34af6c2e4ade4f9fd03a7eb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915420241201Pell Wavelet Optimization Method for Solving Time-Fractional Convection Diffusion Equations Arising in Science and Medicine23925811455010.22052/ijmc.2024.254524.1843ENYadollahOrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranSedighehSabermahaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranMohsenRazzaghiDepartment of Mathematics and Statistics, Mississippi State University, United States of AmericaJournal Article20240310Here, we present a composition method for solving time-fractional convection-diffusion equations (TF-CDEs). The main aims of the technique are to use Pell wavelets and convert the considered problem into fractional partial integro-differential equations, utilizing the Riemann-Liouville fractional integration (RL).<br />For this approach, we consider Pell wavelets as an efficient tool to develop the method. We compute the RL pseudo-operational matrix for these functions. Taking RL for the considered problem and using the properties of RL, with the help of a pseudo-operational matrix and optimization scheme, we present the framework of the suggested scheme. Moreover, for approximate results, we evaluate the upper bound of errors. As a result, we apply the method by solving some numerical samples. Our approximate results illustrate that the computational scheme is powerful and applicable to solve the mentioned problems, and we can implement this to solve different kinds of fractional problems.https://ijmc.kashanu.ac.ir/article_114550_d896f9cbb60353c1dd19f4cd5998d2e0.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915420241201Extremal Chemical Trees for a Modified Version of Sombor Index25926811455810.22052/ijmc.2024.254215.1814ENLkhagvaBuyantogtokhDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, MongoliaBatmendHoroldagvaDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia0000-0003-3417-2612ShiikharDorjsembeDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, MongoliaEnkhbayarAzjargalDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, MongoliaJournal Article20240111Let $G$ be a molecular graph, where $d_u$ representes the degree of vertex $u$, and $uv$ denotes an edge connecting vertices $u$ and $v$. A few years ago, a new vertex-degree-based graph invariant (topological index) was introduced by Gutman, defined as $SO(G)=\sum_{uv\in E}\sqrt{d_u^2+d_v^2}$, called the Sombor index. Recently, Kulli et al. compared several modified versions of Sombor index (Nirmala, Sombor, Dharwad, and $F$-Sombor indices), they found that these indices are highly correlated and their values for QSPR applications are nearly the same. Based on this study Kulli et al. introduced a new vertex-degree-based topological index, which is defined as $X(G)=\sum_{uv\in E}\sqrt{d_u^k+d_v^k}$, where $k\geq 1$ is a real number. In this paper, we determine the extremal chemical trees with respect to $X$ index.https://ijmc.kashanu.ac.ir/article_114558_d54915bc7fa0b004a61ed036cd985633.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915420241201Metric Dimension for Line Graph of Some Chemical Structures26928211457110.22052/ijmc.2024.254131.1817ENR.Nithya RajDepartment of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, IndiaR.Sundara RajanDepartment of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, IndiaIndraRajasinghDepartment of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, 602 105, IndiaIsmail NaciCangulDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle 16059, TurkeyJournal Article20240113The metric dimension of a graph is a fundamental parameter that measures the minimum number of vertices to identify all other vertices in the graph uniquely. In the context of chemical structures, where graphs represent molecular entities, the metric dimension becomes a crucial metric for understanding molecular behavior and interactions. A subset $T = \{ t_1,t_2,\ldots, t_k \}$ of nodes of a connected network $G$ is referred to as a revolving set, if for any pair of nodes, $ l,m \in V(G)$ there exists a node $t \in T$, such that its distances from $l$ and $m$ are different. The smallest {cardinality} of $T$ is referred to as the metric dimension of $G$, and the nodes in $T$ constitute a metric basis of $G$. In this work, we calculate the line graph's metric dimension for some chemical structures such as hexagon-square chains, linear phenylene structures, and linear heptagonal structures.https://ijmc.kashanu.ac.ir/article_114571_95d139e93921baaa7976dd0006ce9f37.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915420241201On Relations between Atom-Bond Sum-Connectivity Index and other Degree-Based Indices28329511457210.22052/ijmc.2024.254522.1842ENShettySwathiDepartment of Mathematics, Manipal Institute of Technology Manipal Academy of Higher Education, Manipal, India -- 576104N. V. Sayinath UdupaDepartment of Mathematics, Manipal Institute of Technology Manipal Academy of Higher Education, Manipal, India -- 576104B. R.RakshithDepartment of Mathematics, Manipal Institute of Technology Manipal Academy of Higher Education, Manipal, India -- 576104LaxmanaAnushaDepartment of Mathematics, Manipal Institute of Technology Manipal Academy of Higher Education, Manipal, India -- 576104Journal Article20240308The atom-bond sum-connectivity $(ABS)$ index is a novel vertex degree-based topological index defined recently as,<br />$ABS(G)=\sum\limits_{i\simj}\sqrt{\frac{d_{i}+d_{j}-2}{d_{i}+d_{j}}}=\sum\limits_{i\sim j}\sqrt{1-\frac{2}{d_{i}+d_{j}}},$ where $d_{i},d_{j}$ are degrees of vertices $i$ and $j$ respectively. New findings linking the $ABS$-index to extensively researched topological indices are presented in this work.https://ijmc.kashanu.ac.ir/article_114572_d1c22589176c11738f73018864452f26.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915420241201The Man Who Knew Symmetry: A Tribute to Ali Reza Ashrafi29731711457310.22052/ijmc.2024.254421.1835ENModjtabaGhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785 - 163, I. R. IranRazie AlidehiRavandiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785 - 163, I. R. IranOttorinoOriActinium Chemical Research, Via Casilina 1626/A, 00133, Rome, ItalyMihaiPutzLaboratory of Computational and Structural Physical-Chemistry for Nanosciences and QSAR, Biology-Chemistry Department, Faculty of Chemistry, Biology, Geography, West University of Timisoara, Pestalozzi Str. No. 16A,RO-300115 Timisoara, Romania \\ Scientific Laboratory of Renewable Energies-Photovoltaics, RD National Institute for Electrochemistry and Condensed Matter (INCEMC-Timisoara), Dr. Aurel Podeanu Str. No. 144, RO-300569 Timisoara, RomaniaJournal Article20240220Growing up in South Tehran, Ali Reza Ashrafi had a fascination with the application of mathematics in other sciences, particularly the symmetry of molecules, despite having no formal training in the subject.<br />Ashrafi was a prominent mathematician who made significant contributions to the study of symmetry in molecular graphs. His work on this subject has had a profound impact on the field of chemistry, helping chemists to better understand the structure and properties of molecules.<br />With great enthusiasm, Ashrafi explains to his students that the symmetry group plays a significant role in everything and that symmetry can be used to predict or explain many of a molecule's chemical properties.https://ijmc.kashanu.ac.ir/article_114573_4dd3498bb7f610209c5a5c2b2063bbae.pdf