2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56458We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.13p, 5 fig.(eps), ref. updated, to appear in Lett.Math.PhysicsHigh Energy Physics - TheoryHigh Energy Physics - PhenomenologyQuantum Algebratext