### Abstract

Purpose - One of the significant underlying principles of nanorobotic systems deals with the understanding and conceptualization of their respective complex nanocomponents. This paper introduces a new methodology to compute a set of optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms based on dynamic programming and greedy algorithm. Design/methodology/approach - Buckyball, C60, is composed of sixty equivalent carbon atoms arranged as a highly symmetric hollow spherical cage in the form of a soccer ball. At first, Wiener, hyper-Wiener, Harary and reciprocal Wiener indices were computed using dynamic programming and presented them as: W(Buckyball) = 11870.4, WW(Buckyball) = 52570.9, Ha(Buckyball) = 102.2 and RW(Buckyball) = 346.9. The polynomials of Buckyball, Hosoya and hyper-Hosoya, which are in relationship with Buckyball s indices, have also been computed. The relationships between Buckyball s indices and polynomials were then computed and demonstrated a good agreement with their mathematical equations. Also, a graph algorithm based on greedy algorithms was used to find some optimal electronic aspects of Buckyball s structure by computing the Minimum Weight Spanning Tree (MWST) of
Buckyball.

Original language | English |
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Pages (from-to) | 387 - 400 |

Number of pages | 14 |

Journal | COMPEL - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 |

## Cite this

Khataee, H. R., Ibrahim, M. Y., Sourchi, S., Eskandari, L., & Teh Noranis, M. A. (2012). Computing optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms.

*COMPEL - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering*,*31*(2), 387 - 400. https://doi.org/10.1108/03321641211200491