Application of quotient graph theory to three-edge star graphs

• URL: http://arxiv.org/abs/2108.05253v1
• Date: Wed, 11 Aug 2021 14:48:52 GMT
• Title: Application of quotient graph theory to three-edge star graphs
• Authors: Vladim\'ir Je\v{z}ek and Ji\v{r}\'i Lipovsk\'y
• Abstract summary: We find quotient graphs for the three-edge star quantum graph with Neumann boundary conditions at the loose ends. These quotient graphs are smaller than the original graph and the direct sum of quotient graph Hamiltonians is unitarily equivalent to the original Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We apply the quotient graph theory described by Band, Berkolaiko, Joyner and Liu to particular graphs symmetric with respect to $S_3$ and $C_3$ symmetry groups. We find the quotient graphs for the three-edge star quantum graph with Neumann boundary conditions at the loose ends and three types of coupling conditions at the central vertex (standard, $\delta$ and preferred-orientation coupling). These quotient graphs are smaller than the original graph and the direct sum of quotient graph Hamiltonians is unitarily equivalent to the original Hamiltonian.

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