Epitaxial synthesis of inorganic nanomaterials on pristine 2D materials is of interest in the development of nanostructured devices and nanocomposite materials, but is quite difficult because pristine surfaces of 2D materials are chemically inert. Previous studies found a few exceptions including AuCN, AgCN, CuCN, and Cu0.5Au0.5CN, which can be preferentially synthesized and epitaxially aligned onto various 2D materials. Here, we discover that Au1/2Ag1/2CN forms diamond-shaped nanocrystals epitaxially grown on pristine graphene surfaces. The nanocrystals synthesized by a simple drop-casting method are crystallographically aligned to lattice structures of the underlying graphene. Our experimental investigations on 3D structures and the synthesis conditions of the nanocrystals imply that the rhombic 2D geometries originate from different growth rates depending on orientations along and perpendicular to 1D molecular chains of Au1/2Ag1/2CN. We also perform in situ TEM observations showing that Au1/2Ag1/2CN nanocrystals are decomposed to Au and Ag alloy nanocrystals under electron beam irradiation. Our experimental results provide an additional example of 1D cyanide chain families that form ordered nanocrystals epitaxially aligned on 2D materials, and reveal basic physical characteristics of this rarely investigated nanomaterial.