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A Note on Observables for Counting Trails and Paths in Graphs

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Journal of Mathematical Modelling and Algorithms

Abstract

We point out that the total number of trails and the total number of paths of given length, between two vertices of a simple undirected graph, are obtained as expectation values of specifically engineered quantum mechanical observables. Such observables are contextual with some background independent theories of gravity and emergent geometry. Thus, we point out yet another situation in which the mathematical formalism of a physical theory has some computational aspects involving intractable problems.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5, Ontario, Canada

    Fotini Markopoulou

  2. Institute for Quantum Computing and Department of Combinatorics & Optimization, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontario, Canada

    Simone Severini

Authors
  1. Fotini Markopoulou
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  2. Simone Severini
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Correspondence to Simone Severini.

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Markopoulou, F., Severini, S. A Note on Observables for Counting Trails and Paths in Graphs. J Math Model Algor 8, 335–342 (2009). https://doi.org/10.1007/s10852-009-9111-7

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  • DOI: https://doi.org/10.1007/s10852-009-9111-7

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