Tight binding parameters for graphene

In this article we have reproduced the tight binding $\pi$ band dispersion of graphene including upto third nearest neighbours and also calculated the partial density of states (due to $\pi$ band only) within the same model. The aim was to find out a set of parameters descending in order as distance towards third nearest neighbour increases compared to that of first and second nearest neighbours with respect to an atom at the origin. Here we have talked about two such sets of parameters by comparing the results with first principle band structure calculation.