Omega polynomial

Cluj polynomials, matching polynomial, and omega polynomial. 

The Omega polynomial is a —> counting polynomial based on the counting of the so-called quasiorthogonal cuts (qoc) of a graph as... 

From the Omega polynomial, two molecular descriptors are derived. The first one, called Cluj-Ilmenau index, denoted as Cl, is derived from the first and second D" derivatives of the... 

The second index, denoted as 0, is calculated from the summation of all the possible Omega polynomial derivatives O at x= 1, and normalized to the first polynomial derivative (which is equal to the number of edges in the graph) ... 

Omega polynomials, their derivatives, and Cl and /q indices for anthracene (a) and phenanthrene (b). PI is the PI index. Straight line segments indicate orthogonal edge cuts. 

The non-Omega polynomial is derived from the Omega polynomial so that to be a complementary quantity as... 

Let G be a connected graph and 5i, 2,..., 5 be the ops strips of G. Then the ops strips form a partition of E(G). The length of ops is taken as maximum. It depends on the size of the maximum fold face/ring Fmax/Rmax considered, so that any result on Omega polynomial will have this specification. 

On Omega polynomial, the Cluj-Ilmenau [John et al (2007)] index, Cl = CI G), was defined ... 

Topology of the dense diamond D5 and lonsdaleite L5 is presented in Tables 11.5-11.10 formulas to calculate Omega polynomial, number of atoms, number of rings and the limits (at infinity) for the ratio of sp C atoms over total number of atoms and also the ratio R[5] over the total number of rings (Table 11.5). Numerical examples are given. 

Table 11.2 Omega polynomial in Diamond Dg and Lonsdaleite Lg nets, function of the number of repeating units along the edge of a cubic (k,k,k) domain Network... 

Table 11.3 Examples, omega polynomial in diamond Dg and lonsdaleite Eg nets... 

Table 11.7 Omega polynomial in D5 28 co-net function of = no. ada 20 units along the edge... 

Table 11.9 Omega polynomial in Lonsdaleite-like L5 28 and L5 20 nets function of k = no. repeating units along the edge of a cubic jk,k,k) domain...

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