A bracket polynomial for graphs, I

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeister equivalence to an equivalence relation on looped graphs. The graph bracket polynomial can be defined recursively using the same pivot and local complementation operations used to define the interlace polynomial, and it gives rise to a graph Jones polynomial V(G)(t) that is invariant under the graph Reidemeister moves.

Title	A bracket polynomial for graphs, I
Creator	Zulli, Louis P.
Creator	Traldi, Lorenzo
Publisher	Journal of Knot Theory and Its Ramifications
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	December 2009
Date Available	2015-05-06T17:24:03Z
Type	Article
Language	English
Keyword	graph
	Kauffman bracket
	Jones polynomial
	Reidemeister move
	knot
	interlace polynomial
	trip matrix
Bibliographic Citation	Traldi, L. and L. P. Zulli (2009 Dec.) "A bracket polynomial for graphis, I." Journal of Knot Theory and Its Ramifications 18 (12): 1681-1709.
Standard Identifier	DOI 10.1142/S021821650900766X
Standard Identifier	Handle 10385/1870
Permalink	http://hdl.handle.net/10385/1870
Rights Statement	In Copyright
Rights Holders	World Scientific Publishing Company