DOI 10.1007/s10910-008-9408-1 ORIGINAL PAPER Omega polynomial and its use in nanostructure description

Abstract A new counting polynomial, called “Omega ” (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-defined on all the normal-ized 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, nano-tubes 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 benz-enoids was found. Omega polynomial is useful in describing the topology of tubular nanostructures