Homfly Polynomial of Knotted Trivalent Plane Graphs

We study the Homfly polynomial of periodic knotted trivalent plane graphs introduced in [1]. We show how periodicity of a knotted trivalent plane graphs is reflected in this polynomial. In particular, we derive congruences of periodic knotted trivalent plane graphs in terms of this polynomial invariant. These congruences yield criteria for periodicity of knotted trivalent plane graphs.

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