University of KashanIranian Journal of Mathematical Chemistry2228-648915320240901Construction of Zero-Divisor Graph of a Hyperlattice with Respect to Hyperideals12313511445010.22052/ijmc.2024.253723.1774ENPallaviPanjarikeDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaKunchamSyam PrasadDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaMaddasaniSrinivasuluDepartment of Chemistry, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaVadirajaBhattaDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaHarikrishnanPanackalDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaJournal Article20231011In this paper, we define the zero-divisor graph of a meet-hyperlattice with respect to a hyperideal. We prove the diameter of a $P-$hyperlattice and Nakano hyperlattice are at most 3 and 4 respectively. We obtain that the zero-divisor graph with respect to the intersection of two prime hyperideals is complete bipartite. We prove certain properties of these zero-divisor graphs with suitable examples.https://ijmc.kashanu.ac.ir/article_114450_4841cf010af8c2155395d97b901295bc.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915320240901The Matrix Transformation Technique for the Time- Space Fractional Linear Schrödinger Equation13715411445110.22052/ijmc.2024.254206.1812ENGholamrezaKaramaliFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad,
Tehran, IranHadiMohammadi-FirouzjaeiFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran0000-0002-7018-500XJournal Article20240109This paper deals with a time-space fractional Schrödinger equation with homogeneous Dirichlet boundary conditions. A common strategy for discretizing time-fractional operators is finite difference schemes. In these methods, the time-step size should usually be chosen sufficiently small, and subsequently, too many iterations are required which may be time-consuming.<br />To avoid this issue, we utilize the Laplace transform method in the present work to discretize time-fractional operators. By using the Laplace transform, the equation is converted to some time-independent problems. To solve these problems, matrix transformation and improved matrix transformation techniques are used to approximate the spatial derivative terms which are defined by the spectral fractional Laplacian operator. After solving these stationary equations, the numerical inversion of the Laplace transform is used to obtain the solution of the original equation. The combination of finite difference schemes and the Laplace transform creates an efficient and easy-to-implement method for time-space fractional Schrödinger equations. Finally, some numerical experiments are presented and show the applicability and accuracy of this approach.https://ijmc.kashanu.ac.ir/article_114451_33ee90f703bf85cf9d6fe28d7ce401be.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915320240901Neighborhood M-Polynomial of Graph Operations: Exploring Nanostructure Applications and Correcting Cycle-Related Graph Results15517411445210.22052/ijmc.2024.253190.1733ENGunajyotiSahariaDepartment of Mathematics, NEHU, Shillong, IndiaJibiteshDuttaMathematics Division, Department of Basic Sciences and Social Sciences, NEHU, Shillong, IndiaSanghitaDuttaDepartment of Mathematics, NEHU, Shillong, IndiaJournal Article20230804Mathematical chemistry is a field of mathematics where chemical compounds are studied by associating a graph to it. A topological index serves as a mathematical invariant that elucidates the underlying topological arrangement of molecules or networks. This paper explores the neighborhood M-Polynomial concerning various graph operations of regular graphs. Additionally, it addresses and rectifies several erroneous results pertaining to cycle-related graphs that were previously reported. Furthermore, we examine the applications of the neighborhood $M$-Polynomial to the $VPHX[m,n]$ nanotubes and $VPHY[m,n]$ nanotori, presenting their potential in real-world. Through this comprehensive investigation, we aim to advance the understanding of topological indices and their practical implications.https://ijmc.kashanu.ac.ir/article_114452_3fb7fc7ca420b1af3fa7b23de35f852a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915320240901Steiner k-Eccentric Connectivity Index: a Novel Steiner Distance-Based Index17518711446210.22052/ijmc.2024.253927.1790ENMedha ItagiHuilgolDepartment of Mathematics, Bengaluru City University, Central College Campus, Bengaluru-560001, IndiaP. H.ShobhaDepartment of Mathematics, Bengaluru City University, Central College Campus, Bengaluru-560001, IndiaJournal Article20231201Let G be a connected graph and S be a k element subset of the vertex set V(G). The Steiner-k distance d_{G}(S) between vertices of S is the minimum size among all connected subgraphs whose vertex set contains S. In this paper, we have defined the Steiner k-eccentric connectivity index and derived a closed formula for the same in case of some standard graphs. Also, we have used Steiner 3-eccentric connectivity index to predict values of boiling point of some primary and secondary amines, cross sectional area and molar refraction of alcohols. For each, regression model is developed and statistical analysis is conducted and these have ensured at least 97\% accuracy.https://ijmc.kashanu.ac.ir/article_114462_05dadde07ce60a5e52e356b64f1d50e2.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915320240901Compared Two Models for Shifted the Gap Energy in Acenes; Quantum Perturbation Theory and Topological Indices18920111446510.22052/ijmc.2024.254055.1804ENBahareAgahi KesheDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranAliIranmaneshDepartment of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, IranJournal Article20240102Acenes, which can be represented by the chemical formula $C_{4n+2} H_{2n+4}$, belong to a group of organic molecules that have attracted significant attention in the fields of electronic molecules and nanoscale research. Investigating their electronic and optical properties, particularly for larger acenes, is a highly resource-intensive and time-consuming endeavor. The objective of this study is to propose a novel approach for analyzing changes in the energy gap using quantum perturbation theory and disorder theory, relying on topological indices. In order to quantify the alterations in the energy gap, the Hamiltonian matrix of spin-orbit interaction, based on quantum perturbation theory, has been utilized. Consequently, the changes in the energy gap between singlet and triplet states, denoted as $E_g$, have been computationally determined for the carbon-carbon bonds. Ultimately, a comprehensive model has been developed to illustrate the variations in the energy gap between singlet and triplet spin states of linear acenes, incorporating the concept of topological indices.https://ijmc.kashanu.ac.ir/article_114465_12072ce36609d38c7400e667770d9aa6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915320240901On the Multiplicative Reformulated First Zagreb Index of n-Vertex Trees with Respect to Matching Number20322511446610.22052/ijmc.2024.253967.1793ENShamailaYousafDepartment of Mathematics, Faculty of Science, University of Gujrat, Gujrat, PakistanAnisaNaeemDepartment of Mathematics, Faculty of Science, University of Gujrat, Gujrat, PakistanJournal Article20231208The multiplicative first Zagreb index is the product of the square of the degree of vertices in a graph $\mathbb{G}$. The multiplicative reformulated first Zagreb index is defined as $\prod_{1,e}(\mathbb{G})= \prod_{x_{1}x_{2}\in E(\mathbb{G})}(d_{\mathbb{G}}(x_{1})+d_{\mathbb{G}}(x_{1})-2)^{2}$, where $E(\mathbb{G})$ is the edge set of a graph $\mathbb{G}$ and $d_{\mathbb{G}}(x_{1})$ is the degree of a vertex $x_{1}$ in a graph $\mathbb{G}$. In this paper, we characterize the minimum and maximum trees and unicyclic graphs with respect to matching and perfect matching using this graph invariant $\prod_{1,e}(\mathbb{G})$ among the collection of all $n$-vertex graphs.https://ijmc.kashanu.ac.ir/article_114466_eb57750789909c208e23764c05e58785.pdf