In this talk, joint work with Bram Mesland on how K-homology classes on Cuntz-Krieger algebras can be represented will be presented. Odd K-homology class are represented as finitely summable Fredholm modules. The idea of the proof is to use the Poincaré duality extension class of Kaminker and Putnam. If time permits, I will place these K-homology classes in the context of Bellissard-Pearson's spectral triples on boundaries of trees, realizing the latter as secondary invariants of the former.