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Order Prime Graphs of Finite Groups Un and K4


Affiliations
1 Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502 Haryana, India
     

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We represent finite group in the form of graphs. These graphs are called order prime graphs. In this paper we shall study order prime graphs of finite groups Un (multiplicative group of integers modulo n) and K4 (Klein's four group).

Keywords

Finite Group, Order Prime Graph.
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  • Akbari S. and Mohammadian A., On zero divisor graphs of finite rings, J. Algebra, 2007; 314: 168-184.

  • Anderson D.F. and Livingston P.S., The zero divisor graph of a commutative ring, J. Algebra, 1999; 217: 434-447.

  • Beck I., Colouring of a commutative ring, J. Algebra, 1988; 116: 208-226.

  • Birkhoff G. and Bartee T.C., Modern Applied Algebra, Mc-Graw Hill, New York, 1970.

  • Bollobas B., Modern Graph Theory, Springer-Verlag, New York, 1998.

  • DeMeyer F.R. and DeMeyer L., Zero Divisor Graphs of Semigroup, J. Algebra, 2005; 283: 190 – 198.

  • Godase A. D., Unit Graph of Some Finite Group Zn, Cn and Dn, International Journal of Universal Science and Technology, 2015; 1(2): 122-130.

  • Godase A. D., 2015, Unit Subgraph of Some Finite Group Zn, Cn and Dn, Research Gate pub. DOI:10.13140/RG.2.1.3415.6648

  • Hall Marshall, Theory of Groups, The Macmillan Company, New York, 1961.

  • Harary F., Graph Theory, Addison Wesley, Reading Mass, 1972.

  • Herrnstein I.N., Topics in Algebra, Wiley Eastern Limited, 1975.

  • Lang S., Algebra, Addison Wesley, 1967.

  • Pankaj, Gunjan and Pruthi M., 2017, Unit Graphs and Subgraphs of Symmetric, Quaternion and Heisenberg Groups, Journal of Information and Optimization Sciences, 38(1), 207-2018.

  • Pankaj, Unit Graphs and Subgraphs of Direct Product of Dihedral and Symmetric Groups, Arya Bhatta Journal of Mathematics and Informatics, 2017; 9(1): 59-70.

  • Sattanathan M. and Kala R., An Introduction to Order Prime Graph, Int. J. Contemp. Math. Sciences, 2009; 4(10): 467 – 474.

  • Smarandache Florentine, Special Algebraic Structures, in Collected Papers, Abaddaba, Oradea, 2000; 3: 78-81.

  • Vasantha Kandasamy, W. B. and Singh S.V., Loops and their applications to proper edge colouring of the graph K2n, Algebra and its applications, edited by Tariq et al, Narosa Pub., 2001; 273-284.


Abstract Views: 299

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  • Order Prime Graphs of Finite Groups Un and K4

Abstract Views: 299  |  PDF Views: 5

Authors

Pankaj
Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502 Haryana, India

Abstract


We represent finite group in the form of graphs. These graphs are called order prime graphs. In this paper we shall study order prime graphs of finite groups Un (multiplicative group of integers modulo n) and K4 (Klein's four group).

Keywords


Finite Group, Order Prime Graph.

References