Graphene has witnessed prodigious interest and growth, since its experimental isolation in 2004. Owing to the outstanding electrical, mechanical and spintronic properties, graphene is considered as a promising candidate for potential applications in future nano-devices. Graphene is intrinsically a zero-gap semi-metal with a linear energy dispersion relation near Dirac points, which limits its applications in semiconducting materials where a suitable bandgap is required. In the pursuit of semiconducting graphene materials, significant advances have been made to generate a sizable bandgap in graphene. One of the successful strategy in this realm is the morphological pattering of 2D graphene sheets into 1D nanoribbons. Graphene nanoribbons (GNRs) are thin, elongated strips of graphene with width less than 100nm. Experimental sophistication's have made possible the synthesis and fabrication of GNRs with different shape and confined width using lithography and chemical techniques. Narrow width GNRs with atomic level control of edge structure have also been synthesized using bottom up chemical synthesis of GNRs from molecular precursors. Depending upon the cutting orientation of edges, two topological conformations, called armchair edged GNR (AGNRs) and zigzag edged GNR (ZGNRs) can be obtained. Both the band gap engineering and magnetic properties of GNRs have been extensively studied. It is well known that when graphene is patterned into graphene nanoribbons, it opens up the energy gap due to confinement of the charge carriers into one dimension. It was shown by Son et al. that band gaps in AGNRs arise from quantum confinement while in zigzag GNRs, it arises from staggered sub-lattice potential due to edge magnetization. Motohiko et al. found that no zero energy states exist for finite length ZGNRs, however the band gap decreases as the length of nanoribbon is increased and zero energy states appears as the length approaches to infinity. Using the tight binding and Hubbard model, Oleg et al. investigated the electronic structure of chiral GNRs wherein the tight binding DOS reveals only one Van-Hove singularities at Fermi level while Hubbard model shows four Van-Hove singularities around Fermi level in the range (-0.15eV,0.15eV). They further demonstrated that the energy gap between first Van-Hove singularities around Fermi level decreases with increase in width of nanoribbon while the energy gap between second Van-Hove singularities around Fermi level remains almost constant.