Bulletin of the
Korean Mathematical Society BKMS

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