Abstract
The dice lattice is the dual lattice of kagome lattice. Many physical properties on the dice lattice have been studied by physicists, such as Ising model, Glassy dynamics of Josephson arrays, and Lattice Green’s function. In this paper, we derive the spectrum and Laplacian spectrum of the dice lattice with toroidal boundary condition. In addition, we apply our results to obtain the formulae of the number of spanning trees, the Kirchhoff index, and the energy of the dice lattice with toroidal boundary condition.
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