Bilangan Kromatik Grap Commuting dan Non Commuting Grup Dihedral

Handrini Rahayuningtyas, Abdussakir Abdussakir, Achmad Nashichuddin

Abstract


Commuting graph is a graph that has a set of points X and two different vertices to be connected directly if each commutative in G. Let G non abelian group and Z(G) is a center of G. Noncommuting graph is a graph which the the vertex is a set of G\Z(G) and two vertices x and y are adjacent if and only if xy≠yx. The vertex colouring of G is giving k colour at the vertex, two vertices that are adjacent not given the same colour. Edge colouring of G is two edges that have common vertex are coloured with different colour. The smallest number k so that a graph can be coloured by assigning k colours to the vertex and edge called chromatic number. In this article, it is available the general formula of chromatic number of commuting and noncommuting graph of dihedral group

Keywords


chromatic number; vertex colouring; edge colouring; commuting and noncommuting graph; dihedral group

Full Text:

PDF

References


G. Chartrand and L. Lesniak, Graph and Digraph 2nd Edition, California: Wadsworth, Inc, 1986.

Abdussakir, N. Azizah and F. Novandika, Teori Graf, Malang: UIN Malang Press, 2009.

A. Abdollahi, S. Akbari and H. Maimani, "Noncommuting Graph of a Group," Journal of Algebra, pp. 468-492, 2006.

M. Raisinghania and R. Aggrawal, Modern Algebra, New Delhi: S. Chand & Company Ltd, 1980.

D. Dummit and R. Foote, Abstract Algebra, New Jersey: Prentice Hall, Inc, 1991.

A. Nawawi and Preeley, On Commuting Graphs for Element of Order 3 in Symetry Groups, Manchester: The Mims Secretary, 2012.




DOI: http://dx.doi.org/10.18860/ca.v4i1.3169

Refbacks

  • There are currently no refbacks.


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

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id
 

Creative Commons License
Cauchy (ISSN: 2086-0382 / E-ISSN: 2477-3344) by http://ejournal.uin-malang.ac.id/index.php/Math is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.