Graph associated with finite groups

Author: lyzl

August undefined, 2024

WebAbstract Let A be a group acting by automorphisms on the group G. The commuting graph of A-orbits of this action is the simple graph with vertex set , the set of all A-orbits on , where two distinct vertices xA and yA are joined by an edge if and only if there exist and such that . The present paper characterizes the groups G for which is an -graph, that is, a … WebWe show that the inverse graph of a finite group is connected if and only if the group has a set of generators whose all elements are non-self-invertible. We also determine the rainbow connection numbers of the inverse graphs of finite groups. ... Inverse graphs associated with finite groups, Electron. J. Graph Theory Appl., 5 (1) (2024), 142 ...

Why do we associate a graph to a ring? - MathOverflow

WebASSOCIATEDWITH A FINITE GROUP ... of many authors is the commuting graph associated with a ﬁnite group. For a ﬁnite group G and X a non-empty subset of G, the commuting graph on X denoted C(G,X) has X as its vertex-set with x,y ∈ X joined by an edge whenever xy = yx. Many authors have studied C(G,X) WebThe power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other. The subgraph of is obtained by deleting the vertex 1 (the identity element of G). In this paper, we first investigate some properties of the power graph and its subgraph . green dot on facebook every two minutes

arXiv:1310.2032v1 [math.GR] 8 Oct 2013

WebNov 18, 2024 · For a finite group G, let $\Delta (G)$ denote the character graph built on the set of degrees of the irreducible complex characters of G. ... ‘ An overview of graphs associated with character degrees and conjugacy class sizes in finite groups ’, Rocky Mountain J. Math. 38 (1) ... WebPseudo-Anosovs of interval type Ethan FARBER, Boston College (2024-04-17) A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional … WebApr 9, 2024 · Distance matrix of enhanced power graphs of finite groups. The enhanced power graph of a group is the graph with vertex set and edge set . In this paper, we compute the spectrum of the distance matrix of the enhanced power graph of non-abelian groups of order , dihedral groups, dicyclic groups, elementary abelian groups $\El … flt god of war

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(PDF) Graphs from Finite Groups: An Overview - ResearchGate

WebThe solubility graph associated with a finite group G is a simple graph whose vertices are the elements of G, and there is an edge between two distinct elements x and y if and … WebFeb 19, 2024 · All groups considered in the present paper are supposed to be finite. The solubility graph \Gamma _S (G) associated with a group G is a simple graph whose vertices are the elements of G , and there is an edge between two distinct elements x and y if and only if the subgroup \langle x,y \rangle is soluble. green dot on facebook business pageWebFeb 24, 2024 · The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices … green dot on food products

"WebApr 9, 2024 · For the non-cyclic abelian group $\El(p^n)\times \El(q^m)$, we also compute the spectrum of the adjacency matrix of its enhanced power graph and the spectrum of the adjacency and the distance ... " - Graph associated with finite groups

Graph associated with finite groups

$arXiv:1310.2032v1 [math.GR] 8 Oct 2013$

Webis the finite cyclic group of order and the set consists of two elements, the standard generator of and its inverse, then the Cayley graph is the cycle . More generally, the Cayley graphs of finite cyclic groups are exactly the circulant graphs. WebThe power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other. The subgraph …

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WebOct 15, 2024 · So the commuting graph of a finite group definitely came up naturally. I am unaware of similar ring theoretic examples. ... There are a community of people who look at graphs associated to groups, rings, semigroups and semirings by taking some subset of the algebraic structure and connecting two elements by am edge if the have some … WebOct 8, 2013 · The power graph of a group is a simple graph whose vertex-set is and two vertices and in are adjacent if and only if or for some positive integer . We also pay …

WebFeb 24, 2024 · For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices and are adjacent iff . We call this graph an equal-square graph … WebJun 1, 2024 · Spectrum of a finite graph is defined as collection of all distinct eigenvalues and their algebraic multiplicity of its matrix. The most related topic in the study of spectrum of finite graph is energy. Energy of a finite graph is defined as sum of …

WebSep 26, 2016 · Graphs from Finite Groups: An Overview. Conference: 53rd Mathematical Association of Nigeria Annual Conference. At: Ahmdu … WebAug 27, 2024 · Recently, Alfuraidan and Zakariya [ 1] introduced and studied the inverse graphs associated with finite groups. They established some interesting graph-theoretic properties of the inverse graphs of some finite groups which further shed more light on the algebraic properties of the groups.

WebNov 14, 2016 · There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and… Expand 5 View 1 excerpt, references background Commuting Graphs Of Dihedral Type Groups ∗ Z. Raza, Shahzad Faizi Mathematics 2014

WebMar 9, 2024 · A finite group 𝐺 is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of 𝐺. ... then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. ... In recent work, Cameron, Manna and Mehatari have studied the finite ... flth1155wllWebB. Akbari, N. Iiyori and A. R. Moghaddamfar, A New Characterization of Some Simple Groups by Order and Degree Pattern of Solvable Graph, Hokkaido Mathematical … green dot on iphone when not using cameraWebOct 1, 2024 · We survey known results on enhanced power graphs of finite groups. Open problems, questions and suggestions for future work are also included. Keywords enhanced power graphs; domination; metric dimension;perfect graphs; forbidden subgraphs Full Text: PDF DOI: http://dx.doi.org/10.5614/ejgta.2024.10.1.6 References green dot official site online mobile banking fltharcWebApr 8, 2024 · The enhanced power graph 풢 e (G) of a group G is the graph with vertex set G such that two vertices x and y are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between undirected … flth225WebDec 31, 2024 · The power graph P(G) of a finite group G is the graph whose vertex set isG, with two elements in G being adjacent if one of them is a power of theother. The … flt group gmbh \\u0026 co. kgWebIn this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper. green dot on iphone by battery