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The generalized Yamada polynomials of virtual spatial graphs. (English) Zbl 1411.57024

The authors present the generalized Yamada polynomial and show that it can be normalized to be a rigid vertex isotopic invariant of virtual spatial graphs and to be a pliable vertex isotopic invariant for virtual spatial graphs with maximum degree at most \(3\). In this paper, the authors consider the connection and difference between the generalized Yamada polynomial and the Dubrovnik polynomial of a classical link and show the generalized Yamada polynomial specializes to a version of the Dubrovnik polynomial for classical links. It is shown that the resulting polynomial can often be used to determine if a virtual link is non-classical.

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
05C31 Graph polynomials
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References:

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