it is a solid state physics question. calculate the Van Hove singularities in graphene and a square lattice in detail.

it is a solid state physics question.calculate the Van Hove singularities in graphene and a square lattice in detail. I am attachted a example article about van Hove singularities how can I find singularities in graphene(hexzagon) and a square lattice? and how can I verify that the found singularities verify Morse potential? please if you have any idea about how can I calculate write me whatever you think.