Partition of \(\pi \)-electrons among the faces of polyhedral carbon clusters
- 60 Downloads
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
Partial support of the Croatian Science Foundation via research project LightMol (Grant no. IP-2016-06-1142) is gratefully acknowledged by T. Došlić.
- 6.T. Došlić, Importance and redundancy in fullerene graphs. Croat. Chem. Acta 75, 869–879 (2002)Google Scholar
- 8.T. Došlić, I. Zubac, Partition of \(\pi \)-electrons among the faces of fullerene graphs and possible applications to fullerene stability. MATCH Commun. Math. Comput. Chem. 80, 267–279 (2018)Google Scholar
- 9.I. Gutman, A.T. Balaban, M. Randić, C. Kiss-Tóth, Partitioning of \(\pi \)-electrons in rings of fibonacenes. Z. Naturforsch. 60a, 171–176 (2005)Google Scholar
- 10.I. Gutman, T. Morikawa, S. Narita, On the \(\pi \)-electron content of bonds and rings in benzenoid hydrocarbons. Z. Naturforsch. 59a, 295–298 (2005)Google Scholar
- 13.I. Gutman, N. Turković, B. Furtula, On distribution of \(\pi \)-electrons in rhombus-shaped benzenoid hydrocarbons. Indian J. Chem. 45A, 1601–1604 (2006)Google Scholar
- 14.L. Lovász, M.D. Plummer, in Matching Theory, North-Holland Mathematics Studies, vol. 121/Annals of Discrete Mathematics, vol. 29 (North-Holland, Amsterdam/New York/Oxford/Tokyo, 1986)Google Scholar
- 19.N. J. A. Sloane, editor, The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org
- 20.D.B. West, Introduction to Graph Theory (Prentice Hall, Upper Saddle River, 1996)Google Scholar