Bull. Korean Math. Soc. 2018; 55(3): 799-808
Online first article March 8, 2018 Printed May 31, 2018
https://doi.org/10.4134/BKMS.b170258
Copyright © The Korean Mathematical Society.
Ayman Aboufattoum, Elsyed A. Elsakhawy, Kyle Istvan, Khaled Qazaqzeh
Kuwait University, Ain Shams University, Louisiana State University, Kuwait University
We generalize some of the congruences in \cite{P} to periodic knotted trivalent graphs. As an application, a criterion derived from one of these congruences is used to obstruct periodicity of links of few crossings for the odd primes $p=3,5,7,$ and 11. Moreover, we derive a new criterion of periodic links. In particular, we give a sufficient condition for the period to divide the crossing number. This gives some progress toward solving the well-known conjecture that the period divides the crossing number in the case of alternating links.
Keywords: Kauffman polynomial, periodic links, knotted trivalent graphs, crossing number, adequate links
MSC numbers: 57M27, 57M15
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd