Supersymmetry on Graphs and Networks

Abstract

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral properties for a class of graph operators which typically encode relevant graph characteristics.

11 pages, Latex, no figures, remark 4.1 added, slight alterations in lemma 5.3, a more detailed discussion at beginning of sect.6 (zero eigenspace)

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