Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 823567, 9 pages
Research Article

The Concept of -Cycle and Applications

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics (CHE), Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics and Statistics, Faculty of Science and Technology, Thepsatri Rajabhat University, Lopburi 15000, Thailand
4Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Received 7 October 2013; Revised 9 December 2013; Accepted 28 December 2013; Published 26 February 2014

Academic Editor: Franck Petit

Copyright © 2014 Umarin Pintoptang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of -cycle is investigated for its properties and applications. Connections with irreducible polynomials over a finite field are established with emphases on the notions of order and degree. The results are applied to deduce new results about primitive and self-reciprocal polynomials.