Noncommutative manifolds from Graph and k-Graph C*-algebras

In [PRen] we constructed smooth (1,∞)-summable semfinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (k,∞)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes’ conditions for noncommutative manifolds.