  Lifshitz-type formulas are obtained for the van der Waals and Casimir
interaction between graphene and a material plate, graphene and an atom or a
molecule, and between a single-wall carbon nanotube and a plate. The reflection
properties of electromagnetic oscillations on graphene are governed by the
specific boundary conditions imposed on the infinitely thin positively charged
plasma sheet, carrying a continuous fluid with some mass and charge density.
The obtained formulas are applied to graphene interacting with Au and Si
plates, to hydrogen atoms and molecules interacting with graphene, and to
single-wall carbon nanotubes interacting with Au and Si plates. The
generalizations to more complicated carbon nanostructures are discussed.
