2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67427In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a partially commutative group and R. Thompson's group $F$. As a result, we prove that all diagram groups are totally orderable.22 pagesGroup TheoryGeometric Topology20F65text