Some examples of quantum graphs

We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space M 2 . Secondly, we apply the theory of 2-cocycle deformations to Cayley graphs of abelian groups. This defi...

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Bibliographic Details
Published in:Letters in mathematical physics 2022-12, Vol.112 (6), Article 122
Main Author: Gromada, Daniel
Format: Article
Language:English
Subjects:
Complex Systems
Concrete construction
Geometry
Graphs
Group theory
Group Theory and Generalizations
Hypercubes
Mathematical and Computational Physics
Original Paper
Physics
Physics and Astronomy
Theoretical
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Summary:We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space M 2 . Secondly, we apply the theory of 2-cocycle deformations to Cayley graphs of abelian groups. This defines a twisting procedure that produces a quantum graph, which is quantum isomorphic to the original one. For instance, we define the anticommutative hypercube graphs. Thirdly, we construct an example of a quantum graph, which is not quantum isomorphic to any classical graph.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-022-01603-5