Rotation of spatial graphs. (English) Zbl 0845.57003
Summary: We study the spatial graph version of the results by R. P. Anstee, J. H. Przytycki and D. Rolfsen [ibid. 32, No. 3, 237-249 (1989; Zbl 0638.57006)] on rotants in link theory by using the Yamada polynomial instead of polynomial invariants for links. We also give results peculiar to the spatial graph theory concerning flatly isotopic planarity.
MSC:
| 57M15 | Relations of low-dimensional topology with graph theory |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
References:
| [1] | Anstee, R. P.; Przytycki, J. H.; Rolfsen, D., Knot polynomials and generalized mutation, Topology Appl., 32, 237-249 (1989) · Zbl 0638.57006 |
| [2] | Jin, G.-T.; Rolfsen, D., Some remarks on rotors in link theory, Canad. Math. Bull., 34, 480-484 (1991) · Zbl 0754.57002 |
| [3] | Kauffman, L. H., State models and the Jones polynomial, Topology, 26, 395-407 (1987) · Zbl 0622.57004 |
| [4] | Kobayashi, K., Reduced degree of Yamada polynomial and planarity of graphs, Sci. Rep. Tokyo Woman’s Christ. Univ., 80-86, 963-974 (1989) · Zbl 0726.57006 |
| [5] | Yamada, S., An invariant of spatial graphs, J. Graph Theory, 13, 537-551 (1989) · Zbl 0682.57003 |
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