.svg){kind=logo}
GRAPH THEORY FOR FINITE FIELDS
Keywords:
group theory, graph theory, finite fields theory.DOI:
https://doi.org/10.17654/0972555524008Abstract
In this paper, we attach certain graphs to both the additive and the multiplication groups of a finite field. Then we prove fundamental decomposition theorem for graphs of finite fields. We ascertain that the characteristic of the field plays a significant role for the parameters of these graphs. We provide some examples of non-complete power graphs for finite fields. Further, we explain our methods and results by tables at the end.
Received: October 10, 2023
Revised: October 28, 2023
Accepted: December 18, 2023
References
J. Abawajy, A. Kelarev and M. Chowdhury, Power graph: a survey, Electronic Journal of Graph Theory and Applications 1(2) (2013), 125-147.
I. Chakrabarty, S. Ghosh and M. K. Sen, Undirected power graphs of semi groups, Semi Group Forum 78 (2009), 410-426.
P. J. Cameron and S. Ghosh, The power graph of a finite group, Discrete Mathematics 311(13) (2011), 1220-1222.
A. Doostabadi and D. Farrokhi, On the connectivity of proper power graphs of finite groups, Communications in Algebra 43(10) (2015), 4305-4319.
A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of groups, Contributions to General Algebra 12(58) (2000), 3-6.
S. K. Maity, Bipartite and planar power graphs of finite groups, Southeast Asian Bulletin of Mathematics 39(4) (2015), 539-543.
E. McKemmie, Power of graphs of finite groups, Part B. Mathematical Extended Essay for FHS Mathematics and Computer Science, Oxford University, Hilary Term, 2014.
M. Mirzargar, A. R. Ashrafi and M. J. Nadjafi-Arani, On the power graph of a finite group, Filomat 26(6) (2012), 1201-1208.
R. P. Panda and K. V. Krishna, On connectedness of power graphs of finite groups, Journal of Algebra and its Applications 17(10) (2017), 1850184.
K. H. Rosen, Discrete Mathematics and its Applications, Monmouth University (and formerly AT and T Laboratories), Eighth ed., McGraw-Hill, New York, NY, 2019.
T. Tamizh Chelvam and M. Sattanatha, Power graph of finite abelian groups, Algebra and Discrete Mathematics 16 (2013), 33-41.
D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 2001.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
