  In this research has been studied the possibility of existence the neutral
triplet collective mode in undoped graphene and graphite without one-cone
approximation. This work tries to study this collective mode from different
points of view. It also studies the effects of on-site Hubbard interaction on
neutral collective mode in honeycomb lattice via two representations
(sub-lattice and eigenvector). The effective long rang interaction in honeycomb
lattice has been introduced for studying the spin collective mode. This work
shows that short and effective long range interactions are not responsible for
the formation of neutral triplet collective mode in graphene without {\it
one-cone} approximation.
