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One and Two-Variable Interlace Polynomials: A Spectral Interpretation

  • Constanza Riera
  • Matthew G. Parker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

We relate the one- and two-variable interlace polynomials of a graph to the spectra of a quadratic boolean function with respect to a strategic subset of local unitary transforms. By so doing we establish links between graph theory, cryptography, coding theory, and quantum entanglement. We establish the form of the interlace polynomial for certain functions, provide new one and two-variable interlace polynomials, and propose a generalisation of the interlace polynomial to hypergraphs. We also prove conjectures from [15] and equate certain spectral metrics with various evaluations of the interlace polynomial.

Keywords

Boolean Function Adjacency Matrix Complete Graph Quantum Entanglement Power Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Constanza Riera
    • 1
  • Matthew G. Parker
    • 2
  1. 1.Depto. de Álgebra, Facultad de MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.Selmer Centre, Inst. for Informatikk, Høyteknologisenteret i BergenUniversity of BergenBergenNorway

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