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 graph, 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.