Shahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201An algorithm for counting the number of periodic points of a family of polynomials249267221910.22061/jdma.2024.11165.1084ENMonirehAkbariDepartment of Mathematics, Faculty of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, I. R. IranMaryamRabiiDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University,Tehran, I. R.
IranJournal Article20241024In this paper we consider the family $f_a(x) = axd(x ā 1) + x$ when $a < 0$ is a real number and d ā„ 2 is an even integer. The function fa has a unique positive critical point. By decreasing the parameter a, the behavior of the orbit of this critical point changes. In this paper we consider two cases. In the first case the orbit of the positive critical point converges to 0 and in the second case the positive critical point is mapped to a repelling periodic point of period 2. In each case we give a recursive formula to determine the number of the periodic points of fa. Also, in each case we introduce an invariant set on which fa is chaotic. We employ conjugacy map and symbolic dynamics in our investigations.https://jdma.sru.ac.ir/article_2219_154c5741cccfb93c0737a3a1ebb04da3.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201A combined efficient method for approximate two-dimensional integral equations269287222010.22061/jdma.2024.11175.1088ENMohsenFallahpourDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, I. R. IranRezaEzzatiDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, I. R. IranElhamHashemizadehDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, I. R. IranJournal Article20241018In this paper, we combine the two-dimensional (2D) Haar wavelet functions (HWFs) with the block-pulse functions (BPFs) to solve the 2D linear Volterra-Fredholm integral equations (2D-L(VF)IE), so we present a new hybrid computational effcient method based on the 2D-HWFs and 2D-BPFs to approximate the solution of the 2D linear Volterra-Fredholm integral equations. In fact, the HWFs and their relations to the BPFs are employed to derive a general procedure to form operational matrix of Haar wavelets. Theoretical error analysis of the proposed method is done. Finally some examples are presented to show the effectiveness of the proposed method.https://jdma.sru.ac.ir/article_2220_127bc144cbde48c234e0b71f21cbc1ac.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201On the weighted bond additive indices of some nanostructures289307222110.22061/jdma.2024.11216.1092ENLijuAlexDepartment of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001, IndiaNavyaPDepartment of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001, IndiaHridyaK CDepartment of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001, IndiaJournal Article20241027Topological indices are a type molecular descriptor which serves as a tool for property analysis of chemical compounds based on their molecular structure. The edge Mostar index is a recently introduced topological index, which serves as a measure of peripherality of graphs. <br />Two new weighted versions of edge Mostar index have been proposed recently, namely additively weighted and multiplicatively weighted edge Mostar indices. In this paper, we determine the explicit expressions of different weighted versions of edge Mostar indices of carbon nanostructures such as $T^1UC_4C_8[p,q]$-lattice, $T^2UC_4C_8[p,q]$-lattice using a variant of cut method.https://jdma.sru.ac.ir/article_2221_91ea83cc86dc4b777c0fdb34b394eeda.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201Comparison of two methods for calculating ranking points using transitive triads309320222210.22061/jdma.2024.11215.1093ENBowenLiuDepartment of Mathematics, Shenzhen MSU-BIT University, Shenzhen, China.Journal Article20241017To date, the feasibility of constructing a complete graph invariant in polynomial time remains uncertain. Therefore, developing fast algorithms for checking non-isomorphism, including heuristic ones, is crucial. Successful implementation of these heuristics involves modifying existing graph invariants and creating new ones, both of which are still pertinent. Many existing invariants enable the distinction of a large number of graphs in real time.<br />This paper introduces an invariant specifically for tournaments, a type of directed graph. Tournaments are interesting because the number of different tournaments, given a fixed order of vertices, matches the number of undirected graphs with the same fixed order. The proposed invariant considers all possible tournaments formed by subsets of vertices from the given digraph with the same set of arcs. For each subset tournament, standard places are calculated and summed to determine the final vertex points, which constitute the new invariant.<br />Our calculations reveal that the new invariant differs from the most natural tournament invariant, which assigns points to each participant. Initial computational experiments show that the smallest pair correlation between sequences representing these two invariants is observed at dimension 15.https://jdma.sru.ac.ir/article_2222_213d2ce73ac88f02715b1ea8a0cfcf48.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201On the Roman domination number of the subdivision of some graphs321333222310.22061/jdma.2024.11309.1099ENRostamYarke SalkhoriImam Khomeini International University, P.O. Box 34148- 96818, Qazvin, I. R. IranEbrahimVatandoostImam Khomeini International University, P.O. Box 34148- 96818, Qazvin, I. R. IranAliBehtoeiImam Khomeini International University, P.O. Box 34148- 96818, Qazvin, I. R. IranJournal Article20241026A Roman dominating function on a graph $G = (V, E)$ is a function $f : V(G) ā {0, 1, 2}$ satisfying the condition that every vertex u for which $f(u) = 0$ is adjacent to at least one vertex v for which $f(v) = 2$. The weight of a Roman dominating function is the value $f(V) = \sum_{uāV(G)}f(u)$. The minimum possible weight of a Roman dominating function on $G$ is called the Roman domination number of $G$ and is denoted by $\gamma_R(G)$. In this paper, and among some other results, we provide some bounds for the Roman domination number of the subdivision graph $S(G)$ of an arbitrary graph $G$. Also, we determine the exact value of $\gamma_R(S(G))$ when $G$ is $K_n$, $K_{r,s} or $K_{n_1,n_2,...,n_k}$.https://jdma.sru.ac.ir/article_2223_0ecf48ce373bf851b0079075c3e8b9f4.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099420241201On Sombor index of extremal graphs335344222410.22061/jdma.2024.11328.1101ENSoheirRouhaniDepartment of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. IranMohammadHabibiDepartment of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. IranMohammad AliMehrpouyaDepartment of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. IranJournal Article20241004Let $ G $ be a finite simple graph. The Sombor index of $ G $ is defined as $ \sum\nolimits_{uv\in E(G)} \sqrt{d_{u}^{2}+d_{v}^{2}} $ where $d_{u}$ and $d_{v}$ represent the degrees of vertices $ u$ and $v$ in $ G $, respectively. The sum of the absolute values of the adjacency eigenvalues defines the energy of a graph. This paper aims to enhance the current connections between the Sombor index and the energy of graphs. Additionally, we provide some upper bounds for the Sombor index of triangle-free, square-free, $K_r$-free and tripartite graphs in terms of order, size and minimum degree.https://jdma.sru.ac.ir/article_2224_a39338d676e40d6f5b626fb37fe096d3.pdf