Density functional theory (DFT) based calculations were performed on seven isomers of Zig-zag shaped Graphene nano-ribbon (ZGNR) containing 46 carbon atoms and 18 hydrogen atoms each, including their symmetry constraints. Various properties of the ZGNR C46H18 isomers, like binding Energy, dipole moment, HOMO-LUMO gap, and the vibrational IR spectra were determined. It was found that the HOMO-LUMO gaps of isomers ISO2 and ISO3 were significantly different from the others; with the lowest value (0.16 eV) for ISO2 and highest for the ISO3 (2.83 eV). Binding energy calculations demonstrate that the most stable isomers are ISO6 and ISO7.