On analyzing the Euclidean graph of FULLERENE C60, we have obtained the automorphism group of the Euclidean graphs of this molecule. It is proven that this group has order 120 and is isomorphic to Z2 x A5, where Z2 is a cyclic group of order 2 and A5 is the alternating group on five symbols.

Extracting pure FULLERENE (C60) from FULLERENE soot was accomplished in two steps. In the first step, extraction was carried out using a Soxhlet extractor. Different solvents, such as toluene, were used in this method. In this process, light and heavy FULLERENEs were separated from impurities such as soot and other compounds. The applied FULLERENE soot was produced using an electric arc method, and the obtained purity was close to 7%. In the next step, FULLERENE C60 can be separated from other FULLERENEs (particularly C70) by column chromatography. The stationary phase in the chromatography column contained a mixture of activated carbon, silica gel, and celite, and in order to achieve a high efficiency for separation, the column was filled with a combination of these compounds. Organic solvents such as chlorobenzene and 1, 2-dichlorobenzene were used as the mobile phase. Several experiments were designed and conducted to obtain optimal conditions, and consequently, the FULLERENE C60 was purified with proper efficiency. In this method, parameters including efficiency, low cost, and simplicity are of great importance in the aim of obtaining an optimized method. As a result, a suitable method with low cost and high efficiency was used in this research.

In this paper, the vibrational properties of FULLERENE hydrides with the chemical formula C60H2n are investigated using a method based on the potential energy of the molecule. The potential used in this methodology is AIREBO (Adaptive Intermolecular Reactive Empirical Bond Order). Using this interatomic potential, some of the most important frequencies of the FULLERENE hydrides, such as the breathing mode frequency, were calculated and then analyzed. It was observed that in addition to the number of hydrogen atoms in the structure, their position on the C60 cage has a significant effect on the natural frequency corresponding to a particular mode shape. The results obtained by this method have been compared and validated with quantum mechanics and experimental observations. The simulations results demonstrate that the proposed method is capable of calculating the vibrational properties of FULLERENE hydrides with high precision and low computational cost.

A tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. In this paper some special polygonal tiling of sphere, nellipsoid, cylinder, and torus as the most abundant shapes of FULLERENEs are investigated.

The effect of derivatives of FULLERENE soot on hydrocarbon fuels was examined. FULLERENE was prepared from commercial soot containing a mixture of FULLERENE (a>7%) with high solubility in petroleum derivatives. The derivatives of FULLERENEs were reacted with fatty amines such as hexadecylamine in the presence and absence of a solvent. The gas phase, solvent free reaction was carried out at reduced pressure and high temperature conditions. Vacuum distillation was used to remove unreacted amines from the products formed. Thus, an excess of hexadecylamine was used to maximize the number of lipophilic substituents in the mixture of FULLERENEs and soot. In the second step, the effects of derivatives of FULLERENE soot as gasoline additives on octane number, fuel consumption and emission of exhaust pollutants were evaluated using standard tests in Peugeot 405, Samand, and Pride engines. The derivatives did not appreciably change octane number and fuel consumption, but somehow affected the exhaust pollutants including CO, HC and NOx in comparison with ordinary gasoline.Furthermore, the effect of formulated gasoline using hexadecylamine FULLERENE package on exhaust pollutants was evaluated in a 150 hour cycle and no precipitate was observed.