Electronic and magnetic properties of 1-D Beryllium chains interacting with Graphene nano-structures are studied at an ab initio level. In particular, linear Beryllium chains present significant dispersion interactions with Graphene Nanoislands. The magnetic properties of the 1-D Beryllium chains, are not destroyed by the interaction with the surface. However, the nature of the ground state depend strongly on the interaction: at long distance, the chain has an anti-ferromagnetic ground state; the ground state becomes ferromagnetic for distances from the surface shorter than about 3 angstrom. The behavior of the Beryllium system can shed light on the more general problem of the interaction of alkali-earth atoms in a 1-D arrangement and Graphene surfaces. (C) 2010 Elsevier B.V. All rights reserved.