• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.779-806
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• 2015

We construct a state model for the two-variable Kauman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in $\mathbb{R}^3$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.799-808
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• 2018

We generalize some of the congruences in [20] 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.