We construct dimer graphs for type D relativistic Toda models by introducing impurities to the Y2N,0 square dimer graphs. By properly placing the impurities and change of canonical variables assigned to the 1-loops on the dimer graph, we introduce the "folding" of the graphs and get the type D relativistic Toda lattice Hamiltonian and monodromy matrix.
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Lee et al. (2024) studied this question.
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