A bracket polynomial for graphs

2008/08/25 by Lorenzo Traldi, Traldi, L., Louis Zulli +1
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0808.3392

openalex publication_date 2008/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 that is invariant under the graph Reidemeister moves.

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