University of KashanIranian Journal of Mathematical Chemistry2228-648915220240601Investigation of the Partition Dimension in Chemical Networks and its Application in Chemistry516311436610.22052/ijmc.2023.253577.1763ENR Nithya RajDepartment of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India0009-0003-1136-2197R Sundara RajanDepartment of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India0000-0002-1851-6334Ismail Naci CangulFaculty of Arts and Science, Bursa Uludag University, Turkey0000 0002 0700 5774Journal Article20230911Partition dimension problems involve dividing a graph's vertex set into a minimum number of disjoint sets so that each vertex is different with respect to the representation from each disjoint set. As a result of the development of this method, a number of applications have arisen in a number of fields such as drug design, navigation of robots, pattern recognition, and image processing. In this paper, we have calculated the partition dimension of oxide and {zigzag benzenoid networks, and the subdivision of benzenoid hydrocarbon and triangular benzene networks.https://ijmc.kashanu.ac.ir/article_114366_61d536a7da849cbf0d55b78084d59304.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915220240601The Laplacian Spectrum of the Generalized $n$-Prism Networks657811436710.22052/ijmc.2023.253926.1789ENMehdi EliasiDepartment of Mathematics, Khansar Faculty, University of Isfahan, IranJournal Article20231201The Laplacian eigenvalues and polynomials of the networks play an essential role in understanding the relations between the topology and the dynamic of networks. Generally, computation of the Laplacian spectrum of a network is a hard problem and there are just a few classes of graphs with the property that their spectra have been completely computed. Laplacian spectrum for $ n$-prism networks was investigated in [Liu et al., Neurocomputing 198 (2016) 69-73]. In this paper, we give a method for calculating the eigenvalues and characteristic polynomial of the Laplacian matrix of a generalized $n$-prism network. We show how such large networks can be constructed from small graphs by using graph products. Moreover, our results are used to obtain the Kirchhoff index and the number of the spanning trees in the generalized $n$-prism networks. We also give some examples of applications, that explain the usefulness and efficiency of the proposed method.https://ijmc.kashanu.ac.ir/article_114367_3482630c7f9fda53ba024ac03095bc72.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915220240601Computation of Some Graph Energies of the Zero-Divisor Graph Associated~ with the Commutative Ring $\mathbb{Z}_{p^{2}}[x]/\langle x^{2} \rangle$799011436810.22052/ijmc.2023.252990.1723ENClement Johnson RayerDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu,
India0000-0003-3652-3965Ravi Sankar JeyarajDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu,
India0000-0001-9094-503XJournal Article20230523Let $\mathcal{R}$ be the commutative ring $\mathcal{R}=\mathbb{Z}_{p^2}[x]/\langle x^{2} \rangle$ with identity and ${Z^{*}}(\mathcal{R})$ be the set of all non-zero zero-divisors of $\mathcal{R}$. Then, $\Gamma(\mathcal{R})$ is said to be a zero-divisor graph if and only if $a \cdot b= 0$ where $a,b \in V(\Gamma(\mathcal{R})) = {Z^{*}}(\mathcal{R})$ and $(a,b) \in E(\Gamma(\mathcal{R}))$. Let $\lambda_1,\lambda_2,\dots,\lambda_n$ be the eigenvalues of the adjacency matrix, and let $\mu_1,\mu_2,\dots,\mu_n$ be the eigenvalues of the Laplacian matrix of $\Gamma(\mathcal{R})$. Then %the energy of $\Gamma(\mathcal{R})$ is defined as the sum of the absolute values of the eigenvalues of the graph $\Gamma(\mathcal{R})$ and the Laplacian energy of $\Gamma(\mathcal{R})$ is the sum of the absolute deviations of its Laplacian matrix's eigenvalues of the graph $\Gamma(\mathcal{R})$. In this paper,<br />we discuss the energy $\mathcal{E}(\Gamma(\mathcal{R}))=\sum_{i=1}^n \abs{\lambda_{i}}$ and the Laplacian energy $\mathcal{LE}(\Gamma(\mathcal{R}))=\sum_{i=1}^n \abs{\mu_{i}-\frac{2m}{n}}$ where $n$ and $m$ are the order and size of $\Gamma(\mathcal{R})$.https://ijmc.kashanu.ac.ir/article_114368_132a6a13f29b3f7e4820d801bd416cb4.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915220240601Retrieving the Transient Temperature Field and Blood Perfusion Coefficient in the Pennes Bioheat Equation Subject to Nonlocal and Convective Boundary Conditions9110511436910.22052/ijmc.2024.254475.1837ENKamal RashediDepartment of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran0000-0001-7826-1954Journal Article20240301In this paper, we delve into a coefficient inverse problem linked to the bioheat equation, a pivotal component in medical research concerning phenomena such as temperature response and blood perfusion during surface heating. By considering factors like heat transfer between tissue and blood in capillaries and incorporating the geometric intricacies of the skin, we confine our analysis to a one-dimensional domain. Our approach involves transforming the original problem into one concerning the reconstruction of a multiplicative source term within a parabolic equation. Subsequently, we utilize integral conditions to derive a specific integro-differential equation, accompanied by the requisite initial and boundary conditions. Leveraging a spectral method, we streamline the modified problem into a linear system of algebraic equations. To accomplish this, we employ appropriate regularization algorithms to obtain stable approximations for the derivatives of perturbed boundary data and to effectively solve the resultant system of equations.https://ijmc.kashanu.ac.ir/article_114369_ebd680198d8ab3c60dfb17278b29f5b8.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915220240601Computation of Topological Indices of Binary and Ternary Trees using Algorithmic Approach10711511437010.22052/ijmc.2024.252698.1701ENKashif ElahiDeanship of Human Resources and Information Technology, Jazan University, Jazan, Saudi Arabia0000-0002-6091-1864Ali AhmadDepartment of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan,
Saudi Arabia0000-0003-3434-9908Muhammad Ahsan AsimDivision of Computing, Analytics and Mathematics School of Science and Engineering University of Missouri-
Kansas City, MO 64110, USARoslan HasniSpecial Interest Group of Modeling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics,
Universiti Malaysia, Terengganu 21030 Kuala Nerus, Terengganu, Malaysia0000-0003-3695-2145Journal Article20230322In this paper, algorithms are used to compute distance-based topological indices for the Complete Binary Tree (CBT) and the Complete Ternary Tree (CTT). Computation of distance-based topological indices is complex for varied heights of CBT and CTT. Hence designed algorithms to compute distance between any-to-any vertex made this possible to compute the required topological indices for CBT and CTT. The distance calculator algorithm designed for this study can also be customized in digital chemical structures, mathematical chemistry, network traffic control in wireless networks, search applications, high bandwidth routing, parse construction in compilers, and memory management.https://ijmc.kashanu.ac.ir/article_114370_40ade979094ee930d4ad5ffa9244111a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648915220240601Maximum Modified Sombor Index of Unicyclic Graphs with Given Girth11712211437210.22052/ijmc.2023.253810.1780ENSethumadhavan NagarajanDepartment of Mathematics, Kongu Arts and Science College (Autonomous), Erode, Tamilnadu-638 1070000-0002-7747-9027A. VijayaDepartment of Mathematics, AVP College of Arts and Science, Tirupur-641 6520009-0005-0349-5736Journal Article20231118For any graph $G$, the modified Sombor index is defined as the reciprocal of the well-known Sombor Index. The girth of $G$, by short $g(G)$, is the length of the smallest cycle in $G$. A graph with exactly one cycle is a unicyclic graph. If it is further, connected, it is a connected unicyclic graph. In this article, we achieved the modified Sombor index for a collection of graphs, connected unicyclic graphs and also obtained the maximum modified Sombor index for the class of unicyclic graphs based on the restrictions by a fixed girth.https://ijmc.kashanu.ac.ir/article_114372_b2f3d5efe1ca8e26c74d8f640f787deb.pdf