Kauffman polynomial of periodic knotted trivalent graphs
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 799-808
Published online May 31, 2018
Ayman Aboufattoum, Elsyed A. Elsakhawy, Kyle Istvan, Khaled Qazaqzeh
Kuwait University, Ain Shams University, Louisiana State University, Kuwait University
Abstract : 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
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