Abstract
We introduce a polynomial for plane graphs, which is proposed to equal the Dubrovnik polynomial of the corresponding alternating link diagrams via the medial construction. Then using this polynomial we define another polynomial for doubly edge-weighted plane graphs, which has a natural connection with Dubrovnik polynomial of links formed from plane graphs by edge-tangle replacements. In the final, via this connection we give an explanation for a result due to Lipson and compute the Dubrovnik polynomials of classical pretzel links.
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