Reduced-graphene oxide (rGO) sheets have been functionalized by covalently linking beta-cyclodextrin (beta CD) cavities to the sheets via an amide linkage. The functionalized beta-CD:rGO sheets, in contrast to rGO, are dispersible over a wide range of pH values (2-13). Zeta potential measurements indicate that there is more than one factor responsible for the dispersibility. We show here that planar aromatic molecules adsorbed on the rGO sheet as well as nonplanar molecules included in the tethered beta-CD cavities have their fluorescence effectively quenched by the beta-CD:rGO sheets. The beta-CD:rGO sheets combine the hydrophobicity associated with rGO along with the hydrophobicity of the cyclodextrin cavities in a single water-dispersible material.