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On the component number of links from plane graphs

Daniel S. Silver

Department of Mathematics and Statistics, University of South Alabama, ILB 325, Mobile, AL 36608, USA

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and

Susan G. Williams

Department of Mathematics and Statistics, University of South Alabama, ILB 325, Mobile, AL 36608, USA

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https://doi.org/10.1142/S0218216515200023Cited by:3 (Source: Crossref)

Abstract

A short, elementary proof is given of the result that the number of components of a link arising from a medial graph M(Γ) by resolving vertices is equal to the nullity of the mod-2 Laplacian matrix of Γ.

Keywords:

AMSC: 05C10, 57M25

References

M. Braverman, R. Kulkarni and S. Roy, Parity problems in planar graphs, Electronic Colloquium on Computational Complexity, Report No. 35 (2007), pp. 1–26 . Google Scholar
C. Godsil and G. Royle , Algebraic Graph Theory ( Springer-Verlag , 2001 ) . Crossref, Google Scholar
C. McA. Gordon and R. A. Litherland , Invent. Math. 47 , 53 ( 1978 ) . Crossref, Web of Science, Google Scholar
L. H. Kauffman , Formal Knot Theory ( Princeton University Press , 1983 ) . Google Scholar
L. H. Kauffman , Knots and Physics , 2nd edn. , Series on Knots and Everything 1 ( World Scientific , 1993 ) . Crossref, Google Scholar
R. H. Kyle , Ann. of Math. 59 , 539 ( 1954 ) . Crossref, Web of Science, Google Scholar
K. R. Lamey, D. S. Silver and S. G. Williams, Vertex-colored graphs, bicycle spaces and Mahler measure, preprint (2014) , arXiv:1408.6570 . Google Scholar
M. Las Vergnas, Graph Theory and Combinatorics, Research Notes in Mathematics 34, ed. R. J. Wilson (Pitman Advanced Publishing Program, 1979) pp. 62–75. Google Scholar
W. B. R. Lickorish , An Introduction to Knot Theory ( Springer , 1997 ) . Crossref, Google Scholar
E. G. Mphako , Proc. Edinburgh Math. Soc. 45 , 723 ( 2002 ) . Crossref, Web of Science, Google Scholar
O. Nanyes , J. Knot Theory Ramifications 6 , 833 ( 1997 ) . Link, Web of Science, Google Scholar
T. Pisanski , T. W. Tucker and A. Žitnik , Discrete Math. 281 , 237 ( 2004 ) . Crossref, Web of Science, Google Scholar
H. Seifert , Math. Ann. 110 , 571 ( 1934 ) . Crossref, Google Scholar