Shahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601On an interesting hypothesis of the theory of formal languages81102215410.22061/jdma.2024.10789.1069ENBorisMelnikovShenzhen MSU-BIT University, ChinaJournal Article20240417The formulation of a hypothesis for any pair of nonempty finite languages is considered. The hypothesis consists in the formulation of the necessary conditions for the equality of infinite iterations of these languages, the paper provides some equivalent versions of this hypothesis. When fulfilling this hypothesis, we show the possibility of verifying the equality of infinite iterations of these languages in polynomial time. On the other hand, we present a plan for reducing the verification of the same equality to checking the completeness of the language of a specially constructed nondeterministic finite automaton, and such a check cannot be carried out in polynomial time. In this regard, the possibility of reducing the equality P=NP to the special hypothesis of the theory of formal languages is formulated.https://jdma.sru.ac.ir/article_2154_549ec79d95e8acb46908f1ef747bb707.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601On the two-sided group digraph with a normal adjacency matrix103111215910.22061/jdma.2024.11041.1072ENFarzanehNowroozi LarkiDepartment of Mathematics, Shahid Rajaee Teacher Training University, Lavizan, Tehran, I. R. IranShahramRayat PishehDepartment of Mathematics, Shahid Rajaee Teacher Training University, Lavizan, Tehran, I. R. IranJournal Article20240401This article explores the adjacency matrix of a two-sided group graph and its properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We also obtain the adjacency matrix of the latter digraph and provide a criterion for determining the normality of the adjacency matrix of a two-sided group graph. Moreover, we prove that if all the two-sided group digraphs of valency two for a certain group G are normal, then G is a Hamiltonian group. We also show that if a strongly connected two-sided group digraph of valency two is normal, the corresponding group is isomorphic to the product of two groups: a cyclic group with either Tk,n or Hp,q, or an abelian group.https://jdma.sru.ac.ir/article_2159_7167ca618944db099250844e8eb87128.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601Exploring the watching system of polyhedral graphs113121216610.22061/jdma.2024.11136.1077ENSheydaMaddahDepartment of Mathematics, Faculty of Science,
Shahid Rajaee Teacher Training University,
Tehran, 16785-163, I. R. IranJournal Article20240805Watching system in a graph $G$ is a finite set $W = {w_1, w_2, ..., w_k}$ where each $w_i$ is a couple $w_i = (v_i, Z_i)$, where $v_i$ is a vertex and $Z_i \subset N_G[v_i]$ such that ${Z_1, ..., Z_k}$ is an identifying system.The concept of watching system was first introduced by Auger in [1]. and this system provide an extension of identifying code in the sense that an identifying code is a particular watching system. In this paper, we determine the watching system of specific graphs.https://jdma.sru.ac.ir/article_2166_87f13f4b66afa2247a5fd66845894b2a.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601Orbit entropy versus the symmetry index123131216710.22061/jdma.2024.11131.1074ENMatthiasDehmerCollege of Artificial Intelligence, Nankai University, Tianjin 300350, ChinaDepartment of Biomedical Computer Science and Mechatronics, UMIT, Hall in Tyrol, AustriaDepartment of Computer Science, Swiss Distance University of Applied Sciences, Brig, SwitzerlandAkad University, School of Engineering & Technology, Heilbronner Strasse 86,70191 Stuttgart, GermanyMaryamJalali-RadDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. IranJournal Article20240401The aim of this paper is to compute the novel counting polynomial, orbit polynomial, the symmetry index and the orbit-entropy of several classes of network.https://jdma.sru.ac.ir/article_2167_459d48d19df2497cff11574b48383117.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601A survey on automorphism groups and transmission-based graph invariants133145216810.22061/jdma.2024.10625.1076ENRezaSharafdiniDepartment of Mathematics, Persian Gulf University, Bushehr 75169, I. R. Iran0000-0002-3171-2209MehdiAzadimotlaghDepartment of Computer Engineering of Jam,
Persian Gulf University, Jam, I. R. IranJournal Article20230802The distance $d(u,v)$ between vertices $u$ and $v$ of a connected graph $G$ is equal to the number of edges in a minimal path connecting them. The transmission of a vertex $v$ is defined by $\sigma(v)=\sum\limits_{u\in V(G)}{d(v,u)}$. A topological index is said to be a transmission-based topological index (TT index) if it includes the transmissions $\sigma(u)$ of vertices of $G$. Because $\sigma(u)$ can be derived from the distance matrix of $G$, it follows that transmission-based topological indices form a subset of distance-based topological indices.<br />In this article we survey some results on the computation of some transmission-based graph invariants of intersection graph, hypercube graph, Kneser graph, unitary Cayley graph and Paley graph.https://jdma.sru.ac.ir/article_2168_093cd7a6c5f1dab29163215580b408b2.pdfShahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099220240601Golden ratio in graph theory: a survey147161216910.22061/jdma.2024.11122.1073ENSaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, I. R. IranNimaGhanbariDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, I. R. IranJournal Article20240412Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More precisely, we review the relevance of this number in topics such as the number of spanning trees, topological indices, energy, chromatic roots, domination roots and the number of domatic partitions of graphs.https://jdma.sru.ac.ir/article_2169_e4e053939ea20799568fae2463e4b419.pdf