Abstract
To a finite, connected, unoriented graph of Betti-number g ≥ 2 and valencies ≥ 3 we associate a finitely summable, commutative spectral triple (in the sense of Connes), whose induced zeta functions encode the graph. This gives another example where non-commutative geometry provides a rigid framework for classification.
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de Jong, J.W. Graphs, spectral triples and Dirac zeta functions. P-Adic Num Ultrametr Anal Appl 1, 286–296 (2009). https://doi.org/10.1134/S2070046609040025
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DOI: https://doi.org/10.1134/S2070046609040025