The electronic band structure of a graphene sheet can be determined using density functional theory DFT calculations. Graphene is a two-dimensional 2D material composed of carbon atoms arranged in a hexagonal lattice. The electronic properties of graphene are unique due to its 2D nature and the presence of orbitals from the carbon atoms.In DFT calculations, the electronic structure of a material is obtained by solving the Kohn-Sham equations, which describe the behavior of electrons in a system. The band structure is then obtained by calculating the energies of these electrons at different points in the Brillouin zone, which is the reciprocal space of the crystal lattice.For graphene, the band structure shows a linear dispersion relation near the K and K' points in the Brillouin zone, which are known as the Dirac points. At these points, the valence and conduction bands touch, and the energy-momentum relation resembles that of massless Dirac fermions. This unique feature gives rise to the exceptional electronic properties of graphene, such as high electron mobility and ballistic transport.In summary, the electronic band structure of a graphene sheet obtained using density functional theory calculations reveals a linear dispersion relation near the Dirac points, where the valence and conduction bands touch. This characteristic is responsible for the remarkable electronic properties of graphene.