On Yamada polynomial of spatial graphs obtained by edge replacements

Miaowang Li; Fengchun Lei; Fengling Li; Andrei Vesnin

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arXiv · 1801.09075

On Yamada polynomial of spatial graphs obtained by edge replacements

Miaowang Li·Fengchun Lei·Fengling Li·Andrei Vesnin

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Abstract

We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described by a system of inequalities. Also, the relation between Yamada polynomial of graphs and the chain polynomial of edge-labelled graphs is obtained.

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Miaowang Li, Fengchun Lei, Fengling Li, Andrei Vesnin. 2018-01-27. On Yamada polynomial of spatial graphs obtained by edge replacements. https://arxiv.org/abs/1801.09075

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