Application of Quotient Graph Theory to Three-Edge Star Graphs
1 Citations•2021•
Vladim'ir Jevzek, Jivr'i Lipovsk'y
Acta Physica Polonica A
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Abstract
Abstract. We apply the quotient graph theory described by Band, Berkolaiko, Joyner and Liu to particular graphs symmetric with respect to S3 and C3 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, δ 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.