Appears in collection : 2024 - T3 - Mini-WS - Computational group theory and applications workshop

In the last years, thorough research has been conducted in order to understand graph properties in terms of group properties of the associated right-angled Artin group (RAAG). These properties should be intrinsic, in the sense that they should not depend on a concrete system of generators of the group. In this talk we will give a general review on the topic, with emphasis in planarity, self-complementarity and existence of surjections. In particular, we will highlight the crucial role of the cohomology algebra of the group in our approach. This is joint work with D. Kahrobaei and T. Koberda.