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In the context of infinite weighted graphs, we consider the discrete Laplacians on 0forms and 1-forms. Using Weyl’s criterion, we prove the relation between the nonzero spectrum of Δ0 and that of Δ1 . Moreover, we give an extension of the work of John Lott to characterize the 0-spectrum of these two Laplacians. Mathematics subject classification (2010): 39A12, 05C63, 05C05, 47A53.

Spectra of Laplacians on forms on an infinite graph