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Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs

Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs

In this paper, we study the Dirichlet-to-Neumann operators on infinite subgraphs of graphs. For an infinite subgraph, we prove Cheeger-type estimates for the bottom spectrum of the Dirichlet-to-Neumann operator, and the higher order Cheeger estimates for higher order eigenvalues of the Dirichlet-to-Neumann operator.