# Partition of \(\pi \)-electrons among the faces of polyhedral carbon clusters

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## Abstract

We apply the concepts of importance and redundancy to compute and analyze the partition of \(\pi \)-electrons among faces of actual and potential polyhedral carbon clusters. In particular, we present explicit formulas and investigate asymptotic behavior of total and average \(\pi \)-electron content of all faces of prisms and *n*-barrels. We also discuss the observed deviations from the uniform distribution and show that the patterns of net migration of \(\pi \)-electrons differ from those computed for narrow nanotubical fullerenes. Some possible directions of future work are also indicated.

## Keywords

\(\pi \)-electron partition Polyhedral carbon cluster Prism graph Perfect matching## Notes

### Acknowledgements

Partial support of the Croatian Science Foundation via research project LightMol (Grant no. IP-2016-06-1142) is gratefully acknowledged by T. Došlić.

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