Hayder Baqer Shelash

University Of Kufa | UOK · Department of Mathematics

In this paper, Create regularly textured images using Texture analysis filters and Walsh Hadamard Transform is presented. In particular, we analyze the effectiveness of the Texture analysis filters and Walsh Hadamard Transform in automatic image annotation and content based imageCreate regularly textured. This algorithm registers images of the same...

In this paper, we introduce a new method to transform image by using irreducible character table for point group 𝐶2 ,𝐶2𝑣by considering character table as square matrix of size 2×2, 4×4, and designing an algorithm for it, which includes the transformation matrix of the image to the sets of matrices square of size 2×2, 4×4

Suppose G is a nite group and max(G), nmax(G), snmax(G), maxn(G) and minn(G) are denoted the number of maximal, normal maximal, self-normalizing maximal, maximal normal and minimal normal subgroups of G, respectively. The aim of this paper is to compute these numbers for certain classes of nite groups.

It is well-known that the number of subgroups of the dihedral group D2n can be computed by (n)+�(n), where (n) and �(n) are the number and summation of all positive divisors of n, respectively. The motivation of our study is taken from a paper by Cavior in 1975 that the author proved this formula for dihedral groups. The zeta function of a group G...

The aim of this paper is to compute the number of subgroups and normal subgroups of the group $U_{2np}=\langle a,b\mid a^{2n}=b^{p}=e, aba^{-1}=b^{-1} \rangle$, where $p$ is an odd prime. Suppose $n=2^r\prod_{1 \leq i \leq s}p_{i}^{\alpha_{i}}$ in which $p_i$'s are distinct odd primes, $\alpha_i$'s are positive integers and $t=\prod_{1 \leq i \leq...

This paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n. The Isolated Vertex Property asserts that for a positive integer n, the SPG γ_sp(G) lacks isolated vertices. The Matrix Degree and Edge Formula provide a matrix representation and calculat...

The Wielandt subgroup of a finite group G is defined as w(G) = ∩H◁◁G NG(H). In this paper, this subgroup is computed for certain finite groups.

This study delves into the algebraic and graphical properties of the semidirect product group C_p ⋉ C_4. We ascertain C_p as a normal subgroup, unlike C_4, and establish an isomorphism for prime p. Additionally, the structure of C_4 ⋉ C_m is explored for even m=2k, revealing four potential isomorphisms based on k values. When p is prime and 4 does...

A graph = (,) with vertices and edges is said to be a Root Cube Mean graph if it is possible to label the vertices with distinct lables () from 1,2, … , + 1 in such a way that when each edge = is labeled with (=) = () () () () , then the resulting edge labels are distinct. Here is called a root cube mean labeling of. In this paper we prove that uni...

The finite group M is an H-group if every subgroup in M is an M-subgroup, and we say M is a j-group if every subgroup in M is a j-subgroup. In this study, we look at some of the characteristics of some dihedral group subgroups. As a result, we have student relationships between several subgroups.the quantity demand and investment in research and de...

The approval of the Ministry of Higher Education and Scientific Research was obtained to accept non-Iraqi students as a scholarship or at a private expense in Iraqi universities, starting from the academic year 2022-2023, within special Regulations and specific competencies, as shown below. https://uokufa.edu.iq/scholarships-application-for-non-ir...

Its well known that there are a limited number of method which associate group theory to graph theory. n this paper, we propose a new method and obtain a novel kind of graphs. Some important application like graph energy was established to the proposed graph.

To gain better understanding of molecules, social nods, urban planning and other networks, we need to represent them as graphs which is why graph theory is a very active area in mathematics. In addition, it is well known that the Fibonacci sequence appears in many different areas. Recently, the Fibonacci and Lucas graphs were introduced and some of...

The aim of this paper is to compute the number of subgroups of the group C p α C 4 , where p is an odd prime and 1 ≤ α ≤ 2. It is proved that the number of subgroups is σ(p α) + 6.

Monad graph is a directed graph related to finite group G where every vertex of the elements of the correspond group G is adjacent with it's image by directed connected edge under the action of given map. In this paper, we introduce multi-monad graph, which is a joint union of finite number of monad graphs.

Monad graph is a directed graph related to finite group G where every vertex of the elements of the correspond group G is adjacent with it's image by directed connected edge under the action of given map. In this paper, we introduce multi-monad graph, which is a joint union of finite number of monad graphs.

Let G be afinitenon-solvablegroupwithsolvabilizerset Sol(G). The solvabilitydegreeof G is theprobabilitythattwoelementsarerandomly chosen solvablegroupsin G denoted as PSol(G). Thisconceptisusedto determine thesolvablegroupofagroup.Theprobabilitycanbeobtained by findingasolvabledegreeelementtableandconjugacyclasses.The concept ofsolvabilitydegreeha...

Let G be a finite group with normal degree, cyclic degree and Sylow degree Nor(G), Cyc(G) and Syl(G) respectively. The normality degree, cyclicity degree and Sylow degree of G is the probability that two elements randomly chosen normal subgroup, cyclic subgroup or Sylow subgroup in G denoted as PNor(G),PCyc(G) and PSyl(G) respectively. This concept...

Let G be a finite group with normal degree, cyclic degree and Sylow degree Nor(G), Cyc(G) and Syl(G) respectively. The normality degree, cyclicity degree and Sylow degree of G is the probability that two elements randomly chosen normal subgroup, cyclic subgroup or Sylow subgroup in G denoted as PNor(G),PCyc(G) and PSyl(G) respectively. This concept...

Let G be a finite non-solvable group with solvable radical Sol(G). The solvable graph Γ sol (G) of group G is a graph with vertex set V (Γ sol) = {σ | σ ∈ G} and two distinct vertices σ 1 and σ 2 are adjacent if and only if σ 1 , σ 2 is solvable group, so the solvability degree of G is define by the number of all elements such that {(σ 1 , σ 2) ∈ G...

Let G be a finite group. The normality degree is given by P nd (G) = |{(x,y)∈G×G| x,y G,∀x,y∈G}| |G| 2 and the normal graph Γ G (V, E) = Γ N is defined by the set of all vertices of E(Γ N) = {{x, y} | x, y G}. In this paper, we establish some properties of the normal graph defined by group D 2n and study the relation between Γ N and P nd (G).

Monad graph is a directed graph related to finite group G where every vertex of the elements of the correspond group G is adjacent with it's image by directed connected edge under the action of given map. In this paper we introduce multi-monad graph.

The types of the subgroups of the groups A5, C2timesA5, C3timesA5, C5timesA5, and CptimesA5, where p is an odd prime integer, were computed and investigated in this study. We divided the subgroups of those groups into four categories: abelian, non-abelian, solvable, and non-solvable. So, for some of those nite groups, we calculated the number of so...

The number of subgroups, normal subgroups and characteristic subgroups of a finite group G are denoted by Sub(G), N Sub(G) and CSub(G), respectively. The main goal of this paper is to present a matrix model for computing these positive integers for dicyclic groups, semi-dihedral groups, and three sequences U 6n , V 8n and H(n) of groups that can be...

In this article, we study the resolvent energy and the pseudospectrum energy of a sequence C12n of fullerenes with exactly 12n carbon atoms. In particular, the resolvent energy of these fullerenes together with their lower bounds are obtained.

In this paper, we introduce a new graph, called subgroup product graph Sub(G) of a group G. The set of vertices of Sub(G) is the set of all subgroups of G V (Sub(G)) = {H i | H i ≤ G, ∀i} and two vertices H i and H j are adjacent if and only if H i ∩ H j = ∅. We characterize when Sub(G) is connected and complete graph.

It is well􀀀known that the number of subgroups of the dihedral group D2n can be computed by (n) + �(n), where (n) and �(n) are the number and summation of all positive divisors of n, respectively. The motivation of the present study is taken from a paper by Cavior and Calhoun where the authors proved this formula for dihedral groups. The cyclic grap...

The Cayley graph Cay(G; S) is a graph from the group G generated by a subset S of G, where the vertices x; y 2 V (Cay(G; S)) are the elements of the group G are join if satisfying the condition x = ys; 9s 2 S. Let G(V;E) be a graph. The common neighbourhood graph of G(V;E) is a graph with vertex set V (G) , in which two vertices v; u are adjacent i...

Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the w...

Let Γ(V,E) be a graph. The Cayley graph of group (G,*) and a subset S is a graph denoted by Cay(G,S), it is with vertex set V(Cay(G,S))=G and two vertices x,y∈G are join if and only if y=xs∈S for some s∈S. In this paper, we obtain characteristics of Cayley graphs under some graph operations, Graph direct product, Graph tenser product, Graph strong...

Let τ(n) is the number of all divisors of n and σ(n) is the number of summation of all divisors n, Cavior , presented the number of all subgroups of the dihedral group is equal by τ(n)+σ(n). We in this paper determines a formula for the number of subgroups, normal and cyclic subgroups of the group G=D_2n×C_p=〈a,b,c|a^n=b^2=c^p,bab=a^(-1),[a,c]=[b,c...

In this paper, we consider a simple graph which is undirected, with no loops or multiple edges. Let G be a graph. We will denote by V (G) and E(G); the set of vertices and edges of G, respectively. The degree of a vertex v 2 V (G) is denoted by deg(v), and it well-known that deg(v) =|N(v)|.

The cyclic graph Γ D 2n ×Cp (V, E) = Γ(C) defined by group D 2n × Cp such that the set of all vertices of Γ(C) are the elements of group D 2n × Cp. V (Γ(C)) = {x|x ∈ D 2n × Cp} is the set of vertices and E(Γ(C)) = {{x, y} | x, y ≤ C D 2n × Cp} is the set of edges where ≤ C is a cyclic subgroup of group D 2n × Cp. The normal graph Γ D 2n ×Cp (V, E)...

Let Γ G,S = Cay(G, S) be a Cayley graph of finite group G. The common neighborhood graph Con(Γ G,S) is a graph with the set of all vertices defined byV (ConΓ G,S) = {x, x ∈ V (Γ {G,s})} and the set of all edges defined by E(ConΓ G,S) = {{x, y} | if N (x) ∩ N (y) = ∅}. The neighborhood of a vertex x denoted by N (x). In this paper, we establish some...

Let 􀀀G;S = Cay(G; S) be a Cayley graph of �nite group G. The common neighborhood graph Con(􀀀G;S) is a graph with the set of all vertices de�ned byV (Con􀀀G;S) = fx; x 2 V (􀀀fG;sg)g and the set of all edges de�ned by E(Con􀀀G;S) = ffx; yg j ifN(x) \ N(y) 6= ;g

Let Γ G,S = Cay(G, S) be a Cayley graph of finite group G. The common neighborhood graph Con(Γ G,S) is a graph with the set of all vertices defined byV (ConΓ G,S) = {x, x ∈ V (Γ {G,s})} and the set of all edges defined by E(ConΓ G,S) = {{x, y} | if N (x) ∩ N (y) = ∅}. The neighborhood of a vertex x denoted by N (x). In this paper, we establish some...

The cyclic graph Γ D 2n ×Cp (V, E) = Γ(C) defined by group D 2n × Cp such that the set of all vertices of Γ(C) are the elements of group D 2n × Cp. V (Γ(C)) = {x|x ∈ D 2n × Cp} is the set of vertices and E(Γ(C)) = {{x, y} | x, y ≤ C D 2n × Cp} is the set of edges where ≤ C is a cyclic subgroup of group D 2n × Cp. The normal graph Γ D 2n ×Cp (V, E)...

Let Γ(V, E) be a graph. The Cayley graph Cay(G, S) of group (G, *) and a subset S is a graph with vertex set V and two vertices x, y are join if and only if y = xs ∈

This research paper determines a formula for the number of subgroups, normal and cyclic subgroups of the group G = D2n × Cp = a, b, c | a n = b 2 = c p , bab = a −1 , [a, c] = [b, c] = 1 , where p is an odd prime number. Subgroup Normal Subgroup Cyclic Subgroup. MSC(2010) 20F12 20F14 20F18 20D15.

Monad graph was introduced by V.I. Arnold in 2003 and many result were investigated in. In this paper is we study the properties of monad graph generated by dynamical system defined on finit group which is isomorphic to C n cyclic group of order n and Dihedral group D 2n. Subject Classification: Primary 94B15, Secondary 22A05.

The Wielandt subgroup of a finite group G is defined as w(G) = T H⊳⊳G NG(H). In this paper, this subgroup is computed for certain finite groups.

Let G be a simple graph of order N. The concept of resolvent energy of graph G, i.e. = ∑ (−) where , , … , are the eigenvalues , was established in: [Resolvent energy of graphs , MATCH Commun. Math. Comput. Chem. 75 (2016) , 279−290]. In this paper, the notion of pseudospectrum energy of graphs will be introduced. This is the set defined as = {∑ |(...

The workshop focuses on the latest advanced topics in Dynamical Systems Theory, Group Theory and Functional Analysis . This event brings together professors, researchers, scholars, and students in the mentioned fields to share experience, foster collaborations across industry and academia. The primary aim of organizing such an event is to continue...

Let G be a nite group and C(G) be a family of representatives of the conjugacy classes of subgroups in G.

It is our pleasure to welcome you in the "2nd International Workshop on Advanced Topics in Dynamical Systems, IWATDS", March 1-2, 2020. The 2nd IWATDS 2020 is a sequel to the Workshop on Advanced Topics in Dynamical Systems Theory 2019 which was organized on third of March 2019 by the Department of Mathematics, Faculty of Computer Science and Math...

We consider the dynamical properties of monad graph defined on a finite commutative group, especially, on cyclic group $C_n$ of order $n$ with linear map of form $f(g)=g^3.$

In this paper, we compute the number of subgroups, normal, cyclic subgroups, maximal, minimal and Sylow subgroups of the group G = D 2n × C 2 .

In this paper we want computed and study subgroup commutative degree, normality degree and cyclicity degree of Dicyclic group í µí±» í µí¿’í µí². It is clear that the subgroups í µí±¯ and í µí±² of a group G we can say that í µí±¯ permutes with í µí±² if í µí±¯í µí±² = í µí±²í µí±¯ and the number of subgroups of the Dicyclic group í µí±» í µí¿’í µ...

In this paper, we study certain properties of fuzzy subgroup many basic propertiesin group theory carried over on fuzzy group ‫الخالصة‬ ‫بعض‬ ‫وضعنا‬ ‫ولقذ‬ , ‫الضبابية‬ ‫السمر‬ ‫على‬ ‫تطبيقها‬ ‫يمكن‬ ‫التي‬ ‫و‬ ‫السمر‬ ‫نظرية‬ ‫في‬ ‫الخىاص‬ ‫بعض‬ ‫دراسة‬ ‫الى‬ ‫البحث‬ ‫يهذف‬ ‫رلك‬ ‫تحقيق‬ ‫اجل‬ ‫من‬ ‫الالزمة‬ ‫الشروط‬