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This paper presents a tight binding and ab initio study of finite graphene nanostructures. The attention is focused on three types of regular convex polygons: triangles, rhombuses, and hexagons, which are the most simple high-symmetry convex structures that can be ideally cut out of a graphene layer. Three different behaviors are evidenced for these three classes of compounds: closed-shells for hexagons; low-spin open-shells for rhombuses; high-spin open-shells for triangles.

The Electronic Structure of Graphene Nanoislands: A CAS-SCF and NEVPT2 Study