Computing optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms

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 agreemen...