Dual graphs and knot invariants

Linear Algebra and Its Applications

Volumn 306, Issue 1-3, 2000, Pages 123-130

  Lien, Magnhild ^a   Watkins, William ^a  

^a CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

05C50; 15A36; 15A63; 57M25; Goeritz matrix; Integral quadratic form; Knot; Laplacian matrix; Signed graph; Unimodular congruence

Indexed keywords

EID: 0034380841     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00248-7     Document Type: Article

References (13)

1. Berman K.A. Bicycles and spanning trees. SIAM J. Algebraic Discrete Math. 7:1986;1-12.
2. Goeritz L. Knoten und quadratishe formen. Math. Z. 36:1933;647-654.
3. R. Grone, M. Merris, W. Watkins, Laplacian unimodular equivalence of graphs, in: Avner Friedman, Willard Miller, Jr. (Eds.), Combinatorial and Graph-Theoretical Problems in Linear Algebra, Institute for Mathematics and Its Applications, vol. 80, Springer, 1993, pp. 175-180.
4. Kaufman L. On knots, Ann. Math. Stud. vol. 115. 1987;Princeton University Press, Princeton.
5. Kneser M., Puppe D. Quadratische formen und verschlingungsinvarianten von knoten. Math. Z. 58:1953;376-384.
6. Kyle R.H. Branched covering spaces and the quadratic forms of links. Math. Ann. 59:1954;539-548.
7. Lickorish W.B.R. An Introduction to Knot Theory. 1997;Springer, New York.
8. K. Murasugi, Knot Theory and Its Applications, Birkhäuser, Boston, 1996 (translated by Bohdan Kurpita).
9. Newman M. Integral Matrices, Pure and Applied Mathematics, vol. 45. 1972;Academic Press, New York.
10. K. Reidemeister, Knotentheorie, Eregeb. Math. Grenzgeb., Springer, Berlin, 1932 (Reprinted Springer 1974).
11. Tutte W.T. Graph theory, Encyclopedia of Mathematics and Its Applications vol. 21. 1984;Cambridge University Press, Cambridge.
12. Watkins W. The Laplacian matrix of a graph: unimodular congruence. Linear and Multilinear Algebra. 28:1990;35-43.
13. Watkins W. Unimodular congruence of the Laplacian matrix of a graph. Linear Algebra Appl. 201:1994;43-49.