2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75944We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite spectral triple. The local index theorem allows us to compute the pairing with $K$-theory. This produces invariants in the $K$-theory of the fixed point algebra, and these are invariants for a finer structure than the isomorphism class of $C^*(E)$.33 pagesFunctional AnalysisOperator Algebras46L80; 58B34text