THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS
DOI:
https://doi.org/10.11113/jt.v79.7608Keywords:
Metabelian group, conjugacy class, conjugacy class graph, conjugate graph, properties of graphAbstract
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. Â
References
Davidoff, G., Sarnak, P and ValeGe A. 2003. Elementary Number Theory, Group Theory and Ramanujan Graphs. 1st Edition. Cambridge: Cambridge University Press.
Rahman, S. F. A. and Sarmin, N. H. 2012. Metabelian Groups of Order At Most 24. Menemui Matematik. 34(1): 77-93.
Fraleigh, J. B. 2002. A First Course in Abstract Algebra. 7th Edition. New Jersey: Pearson.
Bondy, J. A. and Murty, U. S. R. 1982. Graph Theory with Application. 5th Edition. New York: Elsevier Science Publishing Co. Inc.
Godsil, C. and Royle, G. Algebraic Graph Theory. 5th Edition. London: Springer-Verlag.
Erfanian, A and Tolue, B. 2012. Conjugate Graphs of Finite Groups. Discrete Mathematics, Algorithms and Applications. 4(2): 35-43.
Bertram, E. A., Herzog, M. and Mann, A. 1990. On a Graph Related to Conjugacy Classes of Groups. Bulletin London Mathematical Society. 22(6): 569-575.
Miller, G. A. 1944. Relative Number of Non-invariant Operators in a Group. Proeeding of National Acaemic Science USA. 30(2): 25-28.
Omer, S. M. S., Sarmin, N. H., Erfanian, A. and Moradipour, K. 2013. The Probability That an Element of a Group Fixes a Set and the Group Act on Set by Conjugation. International Journal of Applied Mathematics and Statistics. 32(2): 111-117.
Moreto, A., Qian, G and Shi, W. 2005. Finite Groups Whose Conjugacy Class Graphs Have Few Vertices. Archiv der Mathematik. 85(2): 101-107.
Bianchi, M., Herzog, M., Pacifici, E. and Saffirio, G. 2012. On the Regularity of a Graph Related to Conjugacy Classes of Groups. European Journal of Combinatorics. 33: 1402-1407.
Ilangovan, S and Sarmin, N. H. 2013. On Graphs Related to Conjugacy Classes of Some Two-groups. AIP Conference Proceeding. 1522: 872-874.
Moradipour, K., Sarmin, N. H. and Erfanian, A. 2013. On Graph Associated to Conjugacy Classes of Some Metacyclic 2-Groups. Journal of Basic and Applied Scientific Research. 3(1): 898-902.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
