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We introduce the the fractional Laplacian on a subgraph of a graph withDirichlet boundary condition. For a lattice graph, we prove the upper and lowerestimates for the sum of the first $k$ Dirichlet eigenvalues of the fractionalLaplacian, extending the classical results by Li-Yau and Kr\"{o}ger.

Eigenvalue estimates for the fractional Laplacian on lattice subgraphs