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References
J.W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci., U.S.A., 9 (1923) 93–95.
C. Bankwitz, Über die Torsionzahlen der alternierenden Knoten, Math. Ann. 103 (1930) 145–161.
J. Frank-R.F. Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987) 97–108.
P. Freyd, et al., A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. 12 (1985) 103–111.
C. McA Gordon-R.A. Litherland, On the signature of a link, Invent. Math. 47 (1978) 53–69
C. McA Gordon-J. Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 3 (1989), 371–415.
V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335–388.
L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395–407.
W.B.R. Lickorish-K.C. Millett, A polynomial invariant of oriented links, Topology 26 (1987) 107–141.
H.R. Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge. Phil. Soc. 99 (1986) 107–109
H.R. Morton-H.B. Short, The 2-variable polynomial of cable knots, Math. Proc. Cambridge Phil. Soc. 101 (1987), 267–278.
K. Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387–422.
—, Jones polynomials and classical conjecture in knot theory, Topology 26 (1987) 187–194.
—, Jones polynomials and classical conjecture in knot theory (II), Math. Proc. Cambridge Phil. Soc. 102 (1987) 317–318.
—, On invariants of graphs with applications to knot theory, Trans. Amer. Math. Soc. 314 (1989) 1–49.
—, On the signature of a graph. C.R. Math. Rep. Acad. Sci. Canada 10 (1988) 107–111.
—, On the braid index of alternating links, (to appear in Trans. Amer. Math. Soc.).
K. Murasugi-J.H.Przytycki, The index of a graph with applications to knot theory (preprint)
J.H. Przytycki-P. Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1987) 115–139.
D. Rolfsen, Knots and links, Publish or Perish Inc (1976).
M. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987) 287–309.
, Kauffman's polynomial and alternating links, Topology 27 (1988) 311–318.
—, On flypes and alternating tangles, (preprint).
P.Traczyk, On the index of graphs: Index versus cycle index (preprint)
H. Whitney, 2-isomorphic graphs, Amer. J. Math. 55 (1933) 236–244.
S. Yamada, The minimal number of Seifert circles equals the braid index of a link, Inv. math. 89 (1987) 347–356.
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Murasugi, K. (1991). Invariants of graphs and their applications to knot theory. In: Jackowski, S., Oliver, B., Pawałowski, K. (eds) Algebraic Topology Poznań 1989. Lecture Notes in Mathematics, vol 1474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084739
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DOI: https://doi.org/10.1007/BFb0084739
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