  We study the electronic structure of graphene in the presence of either
sevenfolds or eightfolds by using a gauge field-theory model. The graphene
sheet with topological defects is considered as a negative cone surface with
infinite Gaussian curvature at the center. The density of electronic states is
calculated for a single seven- and eightfold as well as for a pair of
sevenfolds with different morphology. The density of states at the Fermi energy
is found to be zero in all cases except two sevenfolds with translational
factor $M\neq 0$.
