In this study, effectiveness of non-ionic block copolymers such as Lugalvan BNO12 and Triton X series (Triton X100 & Triton X405) has been reported for graphene dispersion in aqueous solutions. Stability of the aqueous graphene dispersions is investigated using UV–visible spectroscopy, Rheological, and Conductivity studies. Adsorption isotherms are constructed to determine the amount of polymers adsorbed on the surface of graphene by the spectroscopic analysis. Lugalvan BNO12 has been found to be adsorbed in higher amounts on the graphene surface compared to the Triton X series polymers. Thermogravimetric analysis (TGA) and Fourier Transform Infrared (FTIR) Spectroscopy investigations indicated grafting of polymers chains to the graphene surfaces. The dispersions prepared with optimum concentrations (as determined from adsorption isotherms) of polymers have shown lower viscosity and conductivity values. Lugalvan BNO12 has been found to be a better stabilizer for graphene than the Triton X series dispersants because the former contains two aromatic rings in its structure that acts as an anchoring group and helps in the stabilization of graphene dispersion in comparison to the single aromatic group in the Triton X series. The experimental results reported have shown that the aromaticity of polymeric dispersants plays significant role in the aqueous graphene dispersions. The non-ionic block copolymers that assisted dispersed graphene are potential candidates for the fabrication of various devices such as sensors, batteries, and supercapacitors applications.