Face colorings and chiral face colorings of icosahedral giant fullerenes: C80 to C240

نویسندگانK. Balasubramanian, O. Ori, F. Cataldo, A. R. Ashrafi and M. V. Putz
نشریهFullerenes, Nanotubes and Carbon Nanostructures
شماره صفحات1-12
شماره مجلد29
نوع مقالهFull Paper
تاریخ انتشار2021
رتبه نشریهISI
نوع نشریهچاپی
کشور محل چاپبریتانیا

چکیده مقاله

Combinatorial techniques based on Sheehan’s modification of Pόlya’s theorem and Mȍbius inversion technique together with character cycle indices are applied to face colorings of giant fullerenes. These techniques are applied to icosahedral fullerenes, C80 with a chamfered dodecahedron structure, a chiral fullerene C140, icosahedral C180 and C240 with a chamfered truncated icosahedron geometry. The techniques are shown to provide both achiral and chiral face colorings of giant fullerenes for (a) coloring only pentagons with all hexagons painted white, (b) coloring hexagonal faces with all pentagons kept white, (c) both pentagons and hexagons painted with variable colors from a single set, and (d) both pentagons and hexagons painted with variable colors but chosen from two different sets. We have shown that in order to produce chiral colorings for the Ih fullerenes at least 2 black colors and remaining being white are needed when both pentagons and hexagons are varied. Results provide new insights into facial labeling and facial dynamics of fullerenes, while therefore being fully prepared to be inscribed in the new so called neutrosophical science (of carbon) nano-structural physical-chemistry.

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