Omega Polynomial in Tubular Nanostructures

A new counting polynomial, called the »Omega« Ω(G, x) polynomial, was recently proposed by Diudea on the ground of quasi-orthogonal cut »qoc« edge strips in a polycyclic graph. Within a qoc, not all cut edges are necessarily orthogonal, meaning not all are pairwise codistant. Two topological indices: CI (Cluj-Ilmenau), eventually equal to the well-known PI index, in planar, bipartite graphs, and IΩ are defined on the newly proposed polynomial and exemplified. Closed analytical formulas for Ω(G, x) and CI in polyhex tori and tubes are given