A Note on Observables for Counting Trails and Paths in Graphs

Article

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.

Keywords

Enumeration Paths Cycles Observables Graphity models Grassman variables 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Institute for Quantum Computing and Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

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