Finite Groups with a Disconnectedp-Regular Conjugacy Class Graph

2004 ◽  
Vol 32 (9) ◽  
pp. 3503-3516 ◽  
Author(s):  
Antonio Beltrán ◽  
María José Felipe
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Class Graph

scholarly journals The Laplacian Energy of Conjugacy Class Graph of Some Finite Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 59-65
Author(s):  
Rabiha Mahmoud ◽  
Amira Fadina Ahmad Fadzil ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Dihedral Group ◽  
Dihedral Groups ◽  
Laplacian Eigenvalues ◽  
Laplacian Matrices ◽  
Laplacian Energy ◽  
The Difference ◽  
Generalized Quaternion ◽  
Class Graph

Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.

ON THE DIAMETER OF A p-REGULAR CONJUGACY CLASS GRAPH OF FINITE GROUPS

2002 ◽  
Vol 30 (12) ◽  
pp. 5861-5873 ◽  
Author(s):  
Antonio Beltrán ◽  
María José Felipe
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Class Graph

scholarly journals The conjugacy class graph of some finite groups and its energy

2017 ◽  
Vol 13 (4) ◽  
pp. 659-665 ◽  
Author(s):  
Rabiha Mahmoud ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
General Formula ◽  
Finite Groups ◽  
Adjacency Matrix ◽  
Dihedral Group ◽  
Dihedral Groups ◽  
The Absolute ◽  
Generalized Quaternion ◽  
Class Graph

The energy of a graph which is denoted by  is defined to be the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper we present the concepts of conjugacy class graph of dihedral groups and introduce the general formula for the energy of the conjugacy class graph of dihedral groups. The energy of any dihedral group of order   in different cases, depends on the parity of   is proved in this paper. Also we introduce the general formula for the conjugacy class graph of generalized quaternion groups and quasidihedral groups.

scholarly journals General Form of Domination Polynomial for Two Types of Graphs Associated to Dihedral Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 149-155
Author(s):  
Nabilah Najmuddin ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Complete Graphs ◽  
Dominating Sets ◽  
Dihedral Groups ◽  
Graph Polynomial ◽  
Central Elements ◽  
Domination Polynomial ◽  
Class Graph

A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups.

The Diameter of a Conjugacy Class Graph of Finite Groups

1996 ◽  
Vol 28 (2) ◽  
pp. 141-148 ◽  
Author(s):  
Carlo Casolo ◽  
Silvio Dolfi
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Class Graph

On the Diameter of ap-Regular Conjugacy Class Graph of Finite Groups II

2003 ◽  
Vol 31 (9) ◽  
pp. 4393-4403 ◽  
Author(s):  
Antonio Beltrán ◽  
María José Felipe
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Class Graph

scholarly journals On Some Graphs of Finite Metabelian Groups of Order Less Than 24

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 237-247
Author(s):  
Ibrahim Gambo ◽  
Nor Haniza Sarmin ◽  
Sanaa Mohamed Saleh Omer
Keyword(s):  
Normal Subgroup ◽  
Conjugacy Class ◽  
Finite Groups ◽  
Metabelian Group ◽  
Factor Group ◽  
Conjugacy Classes ◽  
Metabelian Groups ◽  
Abelian Normal Subgroup ◽  
Class Graph

In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not coprime. A group is referred to as metabelian if there exits an abelian normal subgroup in which the factor group is also abelian. It has been proven earlier that 25 non-abelian metabelian groups which have order less than 24, which are considered in this work, exist. In this article, the conjugacy class graphs of non-abelian metabelian groups of order less than 24 are determined as well as examples of some finite groups associated to other graphs are given.

THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS

2016 ◽  
Vol 79 (1) ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Ain Asyikin Ibrahim ◽  
Alia Husna Mohd Noor ◽  
Sanaa Mohamed Saleh Omer
Keyword(s):  
Graph Theory ◽  
Conjugacy Class ◽  
Dihedral Group ◽  
Clique Number ◽  
Conjugacy Classes ◽  
Quaternion Group ◽  
Metabelian Groups ◽  
Dominating Number ◽  
Graph Properties ◽  
Class Graph

In this paper, the conjugacy classes of three metabelian groups, namely the Quasi-dihedral group, Dihedral group and Quaternion group of order 16 are computed. The obtained results are then applied to graph theory, more precisely to conjugate graph and conjugacy class graph. Some graph properties such as chromatic number, clique number, dominating number and independent number are found.   

Classification of finite groups according to their conjugacy class lengths

2019 ◽  
Vol 22 (1) ◽  
pp. 137-156
Author(s):  
Zeinab Foruzanfar ◽  
İsmai̇l Ş. Güloğlu ◽  
Mehdi Rezaei
Keyword(s):  
Conjugacy Class ◽  
Finite Groups

Abstract In this paper, we classify all finite groups satisfying the following property: their conjugacy class lengths are set-wise relatively prime for any six distinct classes.

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