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• Very-few-layer graphene (VFLG) can be produced using facile and green process. • VFLG consists of 1–3 layers which is dominated by single layer graphene. • VFLG has edge chirality of armchairs and zigzag with mean lateral size of ~375.4 nm. • DFT calculations provided pertinent optical/electronic properties of graphene. A defect-free graphene with 1–3 layers (very-few-layer graphene, VFLG) has been successfully produced using a facile and environmentally friendly two-step shear exfoliation method in rotating-blade mixer (kitchen blender) and in high shear rotor–stator mixer. An aqueous solution containing an inexpensive and safe anionic surfactant of sodium lauryl sulphate (SLS) was deployed as the working fluid. Raman spectroscopy (RS) and Raman imaging (RI), density functional theory (DFT) simulation, transmission electron microscopy and high-resolution transmission electron microscopy (TEM-HRTEM), as well as Fourier-transform infrared spectroscopy (FTIR) analyses were used to characterize the samples. Some configurations of mixer setting were applied, and the exfoliation mechanisms were discussed. RS analysis revealed that the exfoliation process in rotating-blade mixer continued by high shear in rotor–stator mixer for 3 h had produced VFLG dominated by a single layer of graphene. The Lorentzian peak fitting of 2D band was well-fitted by a single Lorentzian component at Raman shift of 2651.317 cm−1. The produced VFLG endured the lowest peak intensity ratio of D and G bands (I D /I G) of 0.146 which corresponded with the highest lateral size. RI analysis showed that produced VFLG had edge chirality of armchairs and zigzag terminations. TEM-HRTEM confirmed the presence of VFLG with the highest mean lateral size of ~375.4 nm. DFT calculations provided pertinent optical/electronic properties of graphene in terms of Raman Spectra, density of states (DOS) curve and nuclear magnetic resonance (NMR) shielding tensor. FTIR analysis showed that the exfoliation process did not cause any oxidation, sulphonation, or functional defects on the VFLG. The turbulence and hydrodynamic force in liquid were the critical factors in the exfoliation processes. High-quality VFLG, with a facile, inexpensive, and environmentally friendly synthesis process, rendered this process to be a promising route for large-scale high-quality graphene production. [ABSTRACT FROM AUTHOR]