The adjacency matrix of the conjugate graph of metacyclic 2-groups

Nur Idayu Alimon, Nor Haniza Sarmin, Amira Fadina Ahmad Fadzil

Abstract


Let G be a metacyclic 2-group and gamma(conj,G) is the conjugate graph of G. The vertices of gamma(conj,G) are non-central elements in which two vertices are adjacent if they are conjugate. The adjacency matrix of gamma(conj,G) is a matrix A=[a(i,j)] consisting 0's and 1's in which the entry a(i,j) is 1 if there is an edge between ith and jth vertices and 0 otherwise. In this paper, the adjacency matrix of a conjugate graph of metacyclic 2-groups is presented.

Keywords


Adjacency matrix, conjugacy class, conjugate graph, metacyclic group

Full Text:

PDF

References


Rose, H. E. (2009). A Course on Finite Groups. London: Springer.

Sharma, S. (2007). Graph Theory. India: Discovery Publishing House.

Humphries, S. P. and Skabelund, D. C. (2015). Character tables of metacyclic groups. Glasgow Mathematical Journal. 57(02):387-400.

Dummit, D. S. and Richard M. F. (2004). Abstract Algebra, (3rd ed.). New Jersey : John Wiley and Sons Inc.

Goodman, F. M. (2003). Algebra : Abstract and Concrete (Stressing Symmetry), (2nd ed.). USA : Prentice Hall.

Bondy, J. and Murty, U. (1976). Graph Theory with Applications. U. S. A: The Macmillan Press LTD.

Beuerle, J. R. (2005). An elementary classification of finite metacyclic p-groups of class at least three. Algebra Colloqium. 12(4): 553-562.

Erfanian, A. and Tolue, B. (2012). Conjugate graphs of finite groups. Discrete Mathematics, Algorithms and Applications. 4(2): 35-43.

Bilhikmah, N. H., Sarmin, N. H., Omer, S. M. S. and Mohd Noor, A. H. (2016). The conjugacy classes, conjugate graph and conjugacy class graph of some finite metacyclic 2-groups. Discovery Mathematics. 38(01):1-12.




DOI: http://dx.doi.org/10.11113/mjfas.v13n2.640

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Nur Idayu Alimon

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Copyright © 2016 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website. AmazingCounters.com