Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution View Full Text


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Article Info

DATE

2017-12

AUTHORS

G. Stacey Staples

ABSTRACT

Beginning with a simple graph having finite vertex set V, operators are induced on fermion and zeon algebras by the action of the graph’s adjacency matrix and combinatorial Laplacian on the vector space spanned by the graph’s vertices. When the graph is simple (undirected with no loops or multiple edges), the matrices are symmetric and the induced operators are self-adjoint. The goal of the current paper is to recover a number of known graph-theoretic results from quantum observables constructed as linear operators on fermion and zeon Fock spaces. By considering an “indeterminate” fermion/zeon Fock space, a fermion-zeon convolution operator is defined whose trace recovers the number of Hamiltonian cycles in the graph. This convolution operator is a quantum observable whose expectation reveals the number of Hamiltonian cycles in the graph. More... »

PAGES

3923-3934

References to SciGraph publications

  • 2017-06. Zeons, Orthozeons, and Graph Colorings in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • 2008-09. A New Adjacency Matrix for Finite Graphs in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • 2012-03. Spinorial Formulations of Graph Problems in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10773-017-3381-z

    DOI

    http://dx.doi.org/10.1007/s10773-017-3381-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1084932623


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