Shahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901On the hierarchical product of graphs163171217310.22061/jdma.2024.11171.1085ENWilfried ImrichMontanuniversität Leoben, 8700 Leoben, AustriaGabriela MakarAGH University of Krakow, 30-059 Krakow, PolandJuliana PalmenAGH University of Krakow, 30-059 Krakow, PolandPiotr ZajacAGH University of Krakow, 30-059 Krakow, PolandJournal Article20240802The hierarchical product of graphs is a variant of the Cartesian product. It is associative, not commutative, and finite connected graphs have unique first prime factors with respect to it. We present examples of infinite graphs with different first prime factors, and show that homogeneous trees of finite degree have unique prime factoriza-tions with respect to the hierarchical product. On the way, we pose two problems.https://jdma.sru.ac.ir/article_2173_91c59a2519b519c562b6fd4c715cd22f.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901Automorphism group of a graph constructed from a lattice173179218310.22061/jdma.2024.11157.1082ENShahide MalekpourDepartment of MathematicsBehnam BazigaranDepartment of Mathematics, University of KashanJournal Article20240811Let $L$ be a lattice and $S$ be a $\wedge$-closed subset of $L$. The graph $\Gamma_{S}(L)$ is a simple graph with all elements of $L$ as vertex set and two distinct vertex $x,y$ are adjacent if and only if $x\vee y\in S$. In this paper, we verify the automorphism group of $\Gamma_{S}(L)$ and the relation by automorphism group of the lattice $L$. Also we study some properties of the graph $\Gamma_{S}(L)$ where $S$ is a prime filter or an ideal such as the perfect maching.https://jdma.sru.ac.ir/article_2183_94459280bc24c4573d2e828fbd8ad4ca.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901Calculation of topological indices based on M-polynomial for polytrimethylene terephthalate181190218810.22061/jdma.2024.11138.1078ENZohreh RajabinejadDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan
University, Semnan, Iran.0009-0008-0379-0120Saeed Mohammadian SemnaniDepartment of Mathematics, Statistics and Computer Science0000-0001-6755-4911Journal Article20240801Polytrimethylene terephthalate is an extensively utilized thermoplastic industrial polymer characterized by a low melting point and minimal water absorption and it follows the general molecular formula $(C_{11}H_{10}O_{4}){n}$. It is interesting to chemists and engineering researchers due to its application in various industries, especially in textiles and engineering thermoplastics. In this article, the general formulas of some degree-based topological indices are obtained via M-polynomials for Polytrimethylene terephthalate. Calculating indices via these formulas does not require counting the degree of vertices or edge partitioning and can only be calculated by having the number of Polytrimethylene terephthalate monomers. The obtained results are displayed numerically and graphically, then the topological indices are graphically compared.https://jdma.sru.ac.ir/article_2188_182027831094c18baa060554cc7f264b.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901Configuration sets; a right place for ping-pong arguments191202218710.22061/jdma.2024.11140.1079ENMeisam Soleimani MalekanDepartment of Mathematics,
Faculty of Science,
Shahid Rajaee Teacher Training University0000-0002-4521-1325Journal Article20240806Giving a condition for the amenability of groups, Rosenblatt and Willis first introduced<br />the concept of configuration. In this paper, we investigate the relationship between ping-pong lemma and configuration sets, and show that only one configuration set is enough to ensure that several elements in a group generates a free subgroup of that group. Using only one two-sided configuration sets, we give, in a sense, a generalization of this result to polycyclic or FC-groups. Finiteness and paradoxical decompositions of groups, are other properties which can be characterized with only one configuration set.https://jdma.sru.ac.ir/article_2187_cac182b990b575d6c6314b6fe996ead3.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901On the Cayleyness of bipartite Kneser graphs203210219110.22061/jdma.2024.11145.1080ENSeyed Morteza MirafzalLorestan universityJournal Article20240809For any given $n,k \in \mathbb{N}$ with $ 2k < n, $ the $bipartite\ Kneser \ graph$ $H(n, k)$ is defined as the graph whose vertex set is the family of $k$-subsets and ($n-k$)-subsets of $[n] = \{1, 2,\dots, n\}, $ in which<br />any two vertices are adjacent if and only if one of them is a subset of the other.<br />In this paper, we study some algebraic properties of the bipartite Kneser graph $H(n, k)$. In particular, we determine the values of $n,k$, for which the bipartite Kneser<br />graph $H(n,k)$ is a Cayley graph.https://jdma.sru.ac.ir/article_2191_ebe27caa9f315aea60064568865a1363.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901A discussion of Feng-Liu operator and fixed point theorems on metric space211248218910.22061/jdma.2024.11180.1087ENShehu ShagariMohammedDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, NigeriaAbubakar AlhassanMuhammadDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, NigeriaIbrahim AliyuFulatanDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, NigeriaJournal Article20240804In this paper, a collection of various multi-valued fixed point results using Feng-Liu operator on metric space are examined. Comparative discussion on some of the important ideas, using this operators are presented. Thereafter the handful of potential improvements on the existing literature are proposed.https://jdma.sru.ac.ir/article_2189_c3022196c1fcf487370adb4f4cfe7d2d.pdf