  We illustrate possible topological phases in honeycomb lattice with textures
in electron hopping energy between nearest-neighboring sites and show that they
are characterized by the mirror winding number intimately related to the chiral
(or sublattice) symmetry. Analytic wave functions of zero-energy edge modes in
ribbon geometry are provided, which are classified into even and odd sectors
with respect to the mirror operation with the mirror plane perpendicular to the
edge, and evolve into the topological helical edge states at finite momenta.
Intriguingly our results demonstrate that in order to achieve the topological
phase one can decorate the edge in a way adaptive to the bulk hopping texture.
This paves a new way to tailoring graphene in the topological point of view.
