Face colorings and chiral face colorings of icosahedral giant fullerenes: C80 to C240 |
| |
Authors: | Krishnan Balasubramanian Ottorino Ori Franco Cataldo Ali Reza Ashrafi Mihai V Putz |
| |
Affiliation: | 1. School of Molecular Sciences, Arizona State University, Tempe, AZ, USA;2. kbalu@asu.edu;4. Actinium Chemical Research Srl, Rome, Italy;5. https://orcid.org/0000-0002-0842-2684;6. Faculty of Mathematical Sciences, Department of Pure Mathematics, University of Kashan, Kashan, Iran;7. Laboratory of Structural and Computational Physical-Chemistry for Nanosciences and QSAR, Faculty of Chemistry, Biology, Geography, Biology-Chemistry Department, West University of Timisoara, Timisoara, Romania;8. Laboratory of Renewable Energies-Photovoltaics, R&9. D National Institute for Electrochemistry and Condensed Matter, Timisoara, Romania |
| |
Abstract: | AbstractCombinatorial techniques based on Sheehan’s modification of P?lya’s theorem and M?bius 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. |
| |
Keywords: | Enumeration of face colorings of giant icosahedral fullerenes chirality in face colorings of giant fullerenes combinatorial techniques for giant fullerenes labeling of pentagons and hexagons of fullerenes facial rearrangements |
|
|