Symmetry of graphs and perfect state transfer in Grover walks
- URL: http://arxiv.org/abs/2402.17341v1
- Date: Tue, 27 Feb 2024 09:20:09 GMT
- Title: Symmetry of graphs and perfect state transfer in Grover walks
- Authors: Sho Kubota, Kiyoto Yoshino
- Abstract summary: We study relationships between symmetry of graphs and perfect state transfer in Grover walks.
We characterize circulant graphs up to valency $4$ that admit perfect state transfer.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study relationships between symmetry of graphs and perfect state transfer
in Grover walks. Symmetry of graphs mathematically refers to automorphisms of
graphs. When perfect state transfer occurs between two vertices, the following
two statements hold. One is that automorphisms preserve the occurrence of
perfect state transfer. The other is that the stabilizer subgroups of the
automorphism groups with respect to those two vertices coincide. Using these
results, we completely characterize circulant graphs up to valency $4$ that
admit perfect state transfer. Its proof uses also algebraic number theory.
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