University of KashanMathematics Interdisciplinary Research2538-363910220250601Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph13314311489010.22052/mir.2024.255007.1467ENAliGhalavandDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, I. R. IranAlirezaAshrafiDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, I. R. IranJournal Article20240605In this paper, we deal with calculating the laplacian coefficients of a finite simple graph $G$ with the Laplacian polynomial $\psi(G,\lambda) = \sum_{k=0}^{n}(-1)^{n-k}c_k\lambda^k$. We also explore the relationship between the number of closed walks in a graph and a series of its line graphs with the Laplacian coefficients. Our objective is to find a way to determine the Laplacian coefficients using the number of closed walks in a graph and its line graph. Specifically, we have derived the Laplacian coefficients $c_{n-k}$ of a forest $F$ (where $1 \leq k \leq 6$) in terms of the number of closed walks in $F$ and its line graph.https://mir.kashanu.ac.ir/article_114890_4086ca2b1bbd37b77e9cca3d4e7d2f73.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363910220250601On New Definitions Related to Golden Ratio14515811490610.22052/mir.2025.255732.1484ENMehmetPakdemirliMechanical Engineering Department,
Manisa Celal Bayar University,
Manisa, TurkeyJournal Article20241101New definitions employing the golden ratio as the characteristic parameter are proposed. The definitions are classified into two categories: Geometrical and Physical properties. In the first category, the golden ratio tree is defined, and its properties are discussed through theorems. Then, decaying and growing type golden ratio spirals are proposed and discussed. The equation producing the golden ratio heart in the analytical two-dimensional space is given. Regarding the second category, the golden ratio ball is defined with respect to collisions with the ground and the collision coefficient is determined. Golden ratio damping is another new definition in which the dimensionless damped parameter is determined in terms of the golden ratio. Theorems are posed and proven regarding the properties of the definitions. Numerical solutions in the form of plots are given when necessary.https://mir.kashanu.ac.ir/article_114906_7ff756cba9ee8c11e0d0e0c4f5b9edca.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363910220250601Approximation of a Leading Coefficient in an Inverse Heat Conduction Problem via the Ritz Method15918211491010.22052/mir.2025.256068.1492ENMaryamGhorbaniDepartment of Mathematics,
University of Scince and Technology of Mazandaran,
Behshahr, IranKamalRashediDepartment of Mathematics,
University of Scince and Technology of Mazandaran,
Behshahr, IranJournal Article20241228This paper presents a numerical approach for reconstructing the leading coefficient in an inverse heat conduction problem (IHCP). We consider a one-dimensional heat equation with known input data, including the initial condition, a supplementary temperature measurement at the final time, and two integral observations. By incorporating the terminal condition, the unknown spatially dependent coefficient is eliminated, reducing the problem to a nonclassical parabolic equation. The unknown temperature distribution and its derivatives are approximated and applied to the modified governing equation, which is then discretized using operational matrices of differentiation. To ensure stable derivative estimation, the method is coupled with a regularization technique. A least squares scheme is employed to formulate a nonlinear system of algebraic equations, which is solved using Newton’s method. The reliability of the proposed solution is demonstrated through several numerical examples.https://mir.kashanu.ac.ir/article_114910_55ba5850d43fcadb991c9eaeb8ad7d2b.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363910220250601Global Dominator Chromatic Number of Certain Graphs18319811491410.22052/mir.2025.255889.1487ENHadiNouri SamaniDepartment of Mathematical Sciences,
Yazd University,
Yazd, IranSaeidAlikhaniDepartment of Mathematical Sciences,
Yazd University,
Yazd, IranNimaGhanbariDepartment of Mathematical Sciences,
Yazd University,
Yazd, IranJournal Article20241128For a graph G=(V,E) and a vertex subset $D\subseteq V$, a vertex $v\in V$ is called a dominator of D if v is adjacent to every vertex in D, and an anti-dominator of D if v is not adjacent to any vertex in D. Given a coloring $C=\{V_{1},V_{2},\ldots,V_{k}\}$ of $G$, a color {class $V_{i}$} {is a dominating color class (resp. an anti dominating color class) for a vertex v if v dominates all vertices in $V_i$ (resp. v dominates no vertex in $V_i$)}. A coloring C is a global dominator coloring if each vertex in $G$ has both a dominating and an anti-dominating color class. The global dominator chromatic number, denoted by $\chi_{gd}(G)$, is the minimum number of colors required for a global dominator coloring of $G$. In this paper, we investigate the global dominator chromatic number for various classes of graphs.https://mir.kashanu.ac.ir/article_114914_12743d8012f25420d6677f1412b34f7c.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363910220250601Intuitionistic Fuzzy Ideals in $(m,n)$-Near Rings19922911491510.22052/mir.2025.255768.1485ENFahimehMohammadiDepartment of Mathematical Sciences,
Yazd University,
Yazd, IranBijanDavvazDepartment of Mathematical Sciences,
Yazd University,
Yazd, IranJournal Article20241108In this article, first we review some basic definitions and results about fuzzy sets and intuitionistic fuzzy sets; then we state the definitions of intuitionistic fuzzy (m, n)-sub near rings and intuitionistic fuzzy ideals of (m, n)-near rings, which are generalizations of intuitionistics subrings and intuitionistic fuzzy ideals of rings and near-rings, respectively. We provide several examples for the definitions and discuss and investigate some results in this respect. Finally, we investigate the direct product of intuitionistic fuzzy (m, n)-sub near rings of two (m, n)-near rings and state and prove some results on these topics.https://mir.kashanu.ac.ir/article_114915_07ef0af343043eb5dcf6e91720e9edca.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363910220250601Further Results on Generous Roman Domination23124311491810.22052/mir.2025.256617.1511ENSeyed MahmoudSheikholeslamiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. IranMustaphaChellaliLAMDA-RO Laboratory,
Department of Mathematics,
University of Blida,
B.P. 270, Blida, AlgeriaMariyehKorDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. IranJournal Article20250329Let G=(V(G),E(G)) be a graph and h be a function defined from V(G) to {0,1,2,3}. A vertex x with h(x)=0 is said to be undefended with respect to h if it has no neighbor assigned 2 or 3 under h. The function h is called a generous Roman dominating function (GRD-function) if for every vertex with h(x)=0 there exists at least a vertex y with $h(y)\geq2$ adjacent to x such that the function $\eta:V(G)\rightarrow {0,1,2,3}$, defined by $\eta(x)=\alpha$, $\eta(y)=h(y)-\alpha$, where $\alpha\in\{1,2\}$, and $\eta(z)=h(z)$ if $z\in V(G)-\{x,y\}$ has no undefended vertex. The weight of a GRD-function $h$ is the value $\sum_{x\in V(G)}h(x)$, and the minimum weight of a GRD-function on G is the generous Roman domination number (GRD-number) of G. In this paper, we determine the exact value of the GRD-number for the ladder graphs, and we provide an upper bound on it for trees in terms of the order, the number of leaves and the number of stems. Moreover, we show that for every tree on at least three vertices, the GRD-number is bounded below by the domination number plus 2, and we characterize the extremal trees attaining this lower bound.https://mir.kashanu.ac.ir/article_114918_2db2a7d33caddb77c1b45714d0b04c24.pdf