University of KashanMathematics Interdisciplinary Research2538-363911220260601Stability of 2-Domination Number of a Graph11312411552310.22052/mir.2025.257573.1540ENMazharMehrabanDepartment of Mathematical Sciences, Yazd University, 89195-741 Yazd, IranSaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741 Yazd, IranJournal Article20250913This paper delves into the stability of the 2-domination number in simple undirected graphs. The 2-domination number of a graph G, $\gamma_2(G)$, represents the minimum size of a vertex subset where every other vertex in the graph is adjacent to at least two members of the subset. We define the $2$-domination stability, $st_{\gamma_2}(G)$, as the smallest number of vertices whose removal causes a change in $\gamma_2(G)$. Our primary contributions include computing this parameter for specific graphs, establishing various bounds for this stability, and determining its behavior under certain graph operations combining two graphs.https://mir.kashanu.ac.ir/article_115523_49a900eb52a696be092b9696b186f8c1.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363911220260601Perfect Star Packings in (2,6)-Fullerene Graphs12514011552410.22052/mir.2025.257713.1546ENMeysamTaheriUniversity of Applied Science and Technology, Tehran, I. R. IranJournal Article20251006A (2,6)-fullerene graph is a planar and cubic graph with hexagonal and 2-length faces. A perfect star packing is a spanning subgraph of a graph $G$ in which each component is isomorphic to the star graph $K_{1,3}$. In this paper, we investigate which (2,6)-fullerene graphs allow such packings.https://mir.kashanu.ac.ir/article_115524_c4ce5f3f5cca3168695cd89e051a3154.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363911220260601A High-Performance Block-Based Computational Scheme for Solving Fractional Nonlinear Equations in Electrospinning Modeling14115911553510.22052/mir.2026.257657.1542ENHadisAzinDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, I. R. IranYadollahOrdokhanDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, I. R. IranJournal Article20250925The Bratu-type equation of fractional order possesses considerable theoretical and applied importance, as it generalizes a conventional nonlinear differential equation to model phenomena that exhibit inherent memory and non-local interactions, which are crucial in fields such as nuclear reactor assessment and the electrospinning process of nanofibers. This study presents an innovative block-by-block (multi-step) computational methodology that employs quadratic interpolation to attain high-order accuracy. The approach ensures a convergence rate of order $\mathcal{O}(\tau^{4})$, significantly enhancing numerical precision concerning the discretization parameter $\tau$. Its practical utilization is illustrated through a dedicated algorithm tailored for the fractional Bratu problem. The effectiveness and robustness of the proposed method are validated through numerical experiments, showcasing its ability to deliver high-fidelity solutions.https://mir.kashanu.ac.ir/article_115535_82e493d701eec2022830cb861abcc1fd.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363911220260601k-Fibonacci and k-Lucas Differential Equations with New Spirals16117611553610.22052/mir.2026.257640.1541ENMehmetPakdemirliMechanical Engineering Department, Manisa Celal Bayar University, Muradiye, Yunusemre, Manisa, TurkeyİhsanDolapciMechanical Engineering Department, Manisa Celal Bayar University, Muradiye, Yunusemre, Manisa, TurkeyJournal Article20250922Fibonacci sequences and the spirals formed by employing them have found vast applications in creations and natural phenomena. In this study, new k-Fibonacci and k-Lucas differential equations are proposed. First, the k-Fibonacci and k-Lucas sequences are expressed as difference-differential equations. Then, from the difference-differential equations, the associated continuous differential equations are derived, which are linear second-order differential equations. The initial conditions for the differential equations are written with inspiration from the k-Fibonacci and k-Lucas sequences. The solutions, which are new spirals, are expressed in polar form. The spirals produce approximately the k-Fibonacci and k-Lucas numbers at constant steps of angular displacements.https://mir.kashanu.ac.ir/article_115536_7cb311a2267d6aab13c8cd60b661f84b.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363911220260601g(x)-p-Clean Rings17718411553710.22052/mir.2026.257202.1526ENFatemehRashediDepartment of Basic Sciences,
Technical and Vocational University (TVU), Tehran, IranJournal Article20250715Let $R$ be a unital additive ring, C(R) denote the center of the ring R and g(x) be a polynomial in<br />$ C(R)[x] $. We explore a new ring structure called a g(x)-p-clean ring. An element r is said to be g(x)-p-clean if it can be decomposed into r = p + s, where p belongs to the set of pure elements Pu(R), and s is a root of the polynomial $ g(x) $. This study examines the core properties of such rings. We show, for instance, that if R admits the g(x)-p-clean property and I is an ideal of R, then the quotient ring R/I also inherits this property provided $\overline{ g}(x)\in C(R/I)[x]$. We establish a number of structural results concerning these rings.https://mir.kashanu.ac.ir/article_115537_9ba44fa70ddf41ac4563631b013b1686.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363911220260601Estrada Index and Some Properties of Partially Signed Graphs18519911553810.22052/mir.2025.256040.1490ENShilaRazaviDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317-53153 I. R. IranGholam HosseinFath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317-53153 I. R. IranJournal Article20241231A signed graph is a graph with signed edges. Recently, a special graph consisting of signed and unsigned edges has been introduced and is called a partially signed graph. Also, some properties of particular types of these graphs have been discussed. Now, in this article, we pursue some other features of other types of partially signed graphs, such as unicyclic and bipartite partially signed graphs and investigate the reconstruction of the characteristic from their polynomial decks.https://mir.kashanu.ac.ir/article_115538_d3c1ffbb412bba23a02fe19bd167db86.pdf