Omega polynomial and its use in nanostructure description

摘要

A new counting polynomial, called “Omega” Ω (G, x), was recently proposed by Diudea. It is defined on the ground of quasi-orthogonal cut “qoc” edge strips. Three topological descriptors: (1) CI (Cluj-Ilmenau), eventually equal to the well-known PI index, in planar, bipartite graphs; (2) I _Ω-defined on all the normalized derivatives of the above polynomial and (3) the coefficient of the first power term, called n _p are exemplified and used in nanostructures (e.g., fullerenes, nanotubes and tori) description. Good ability of these descriptors in predicting the heat of formation and strain energy in small fullerenes or the resonance energy in planar benzenoids was found. Omega polynomial is useful in describing the topology of tubular nanostructures.