  Moving, merging and annihilating Dirac points are studied theoretically in
the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor
hoppings. We obtain a rich phase diagram of the topological phase transitions
in the parameter space of direction-dependent hoppings. We obtain the
conditions for the three Dirac points to merge and for the tricritical points.
We find that only very small third-nearest-neighbor hoppings are enough for the
existence of the merging of three-Dirac-points and the tricritical points, if
the system is sufficiently anisotropic. The density of states is obtained to be
$D(\epsilon) \propto |\epsilon|^{1/3}$ when three Dirac points merge, and
$D(\epsilon) \propto |\epsilon|^{1/4}$ at the tricritical points. It is
possible to realize these topological phase transitions in the ultracold atoms
on the optical lattice, strained monolayer graphene or strained bilayer
graphene.
