Let be a simple finite connected graph, where V and E are the sets of vertices and edges, respectively. The distance between two vertices u and v in a graph G is the length of the shortest path connecting them, it is denoted by. Two edges and in graph G are said to be codistant if they satisfy the following condition 
If the edges e and f are codistant we write it as e co f. Relation co is reflexive and symmetric but generally not transitive. If co relation is transitive then it is an equiva- lence relation. A graph G in which co is an equivalence relation is called co-graph, and the subset of edges is called an orthogonal cut (oc) of G, also the edge set can be written as the union of disjoint orthogonal cuts, i.e.
Let be two edges of G which are opposite or topologically parallel and denote this relation by e op f. A set of opposite edges, within the same ring eventually forming a strip of adjacent rings, is called an opposite edge strip ops, which is a quasi orthogonal cut (qoc). The length of ops is maximal irrespective of the starting edge. Let be the number of ops strips of length c.
The physico-chemical properties of chemical compounds are often modeled by means of molecular graph based structure descriptors, known as topological indices  ,  . The Wiener index is the first distance based topological index  . The Wiener index of a graph G is defined as
M. V. Diudea introduced the Omega Polynomial for counting ops strips in graph G 
First derivative of Omega polynomial at equals the size of the graph G, i.e.
The Cluj-Ilumenau index  is defined with the help of first and second derivative of Omega polynomial at as
The Omega index is defined as
2. Discussion and Main Result
Polycylic Aromatic Hydorcarbons () are a group of more than 100 different chemicals, these are formed during the incomplete burning of coal, oil, gas, garbage or other substances. are usually found as a mixture containing two or more of these compounds. For further information and results on and other molecular graphs and nano-structures, we refer  -  . In this section, we computed the Omega and Cluj-Ilumenau index of Polycyclic aromatic hydrocarbons.
Theorem 1. Consider the graph of Polycyclic aromatic hydrocarbons, then we have the following
Proof Consider the general representation of the Polycyclic aromatic hydrocarbons as shown in Figure 1. The structure of contain atoms/vertices and bonds/edges.
To obtain the required result, we used the Cut Method  -  . We calculated the for all opposite edge strips. From Figure 2, it is clear that there are distinct cases of qoc strips for and the graph of Polycyclic aromatic hydro- cabons’s graph is a co-graph. The size of a qoc strip is for
and. Because there are co-distant edges with
Figure 1. General representation of polycyclic aromatic hydro- carbons.
Figure 2. A quasi orthogonal cuts strips on polycyclic aro- matic hydrocarbons.
. Also from Figure 2 one can notice that the number of repetition of these qoc stips is six and the number of repetition of is three times. i.e.
・ For, and
・ For all, and
・ For, and
From this, we obtain that
This gives that the Omega polynomial of the Polycyclic aromatic hydrocarbons for all non-negative integer number t is equal to
Now with the help of above polynomial we will investigate the Cluj-Ilmenau and Omega indices of Polycyclic aromatic hydrocarbons.
 Alaeiyan, M., Farahani, M.R. and Jamil, M.K. (2016) Computation of the Fifth Geometric Aithmetic Index for Polycyclic Aromatic Hydrocarbons . Applied Mathematics and Nonlinear Sciences, 1, 283-290. http://dx.doi.org/10.21042/AMNS.2016.1.00023
 Farahani, M.R., Jamil, M.K., Kanna, M.R.R. and Kumar, R.P. (2016) Computation on the Fourth Zagreb Index of Polycyclic Aromatic Hydrocarbons . Journal of Chemical and Pharmaceutical Research, 8, 41-45.
 Farahani, M.R., Jamil, M.K. and Kanna, M.R.R. (2016) The Multiplicative Zagreb eccentricity Index of Polycyclic Aromatic Hydrocarbons . International Journal of Scientific and Engineering Research, 7, 1132-1135.
 Farahani, M.R., Rajesh Kanna, M.R., Pradeep Kumar, R. and Wang, S. (2016) The Vertex Szeged Index of Titania Carbon Nanotubes TiO2(m,n). International Journal of Pharmaceutical Sciences and Research, 7, 1000-08.
 Jamil, M.K., Farahani, M.R., Imran, M. and Malik, M.A. (2016) Computing Eccentric Version of Second Zagreb Index of Polycyclic Aromatic Hydrocarbons . Applied Mathematics and Nonlinear Sciences, 1, 247-251. http://dx.doi.org/10.21042/AMNS.2016.1.00019
 Wang, S.H., Farahani, M.R., Kanna, M.R.R., Kumar, R.P. (2016) Schultz Polynomials and Their Topological Indices of Jahangir Graphs J2,m. Applied Mathematics (Scientific Research Publishing), 7, 1632-1637. http://dx.doi.org/10.4236/am.2016.714140
 Wang, S., Farahani, M.R., Rajesh Kanna, M.R. and Pradeep Kumar, R. (2016) The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs. Applied and Computational Mathematics, 5, 138-141. http://dx.doi.org/10.11648/j.acm.20160503.17
 Wang, S., Farahani, M.R., Baig, A.Q. and Sajja, W. (2016) The Sadhana Polynomial and the Sadhana Index of Polycyclic Aromatic Hydrocarbons PAHk. Journal of Chemical and Pharmaceutical Research, 8, 526-531.
 Yan, L., Li, Y., Farahani, M.R., Jamil, M.K. and Zafar, S. (2016) Vertex Version of Co-PI Index of the Polycyclic Armatic Hydrocarbon Systems PAHk. International Journal of Biology, Pharmacy and Allied Sciences, 5, 1244-1253.
 John, P.E., Khadikar, P.V. and Singh, J. (2007) A Method of Computing the PI Index of Benzenoid Hydrocarbons Using Orthogonal Cuts. Journal of Mathematical Chemistry, 42, 27-45. http://dx.doi.org/10.1007/s10910-006-9100-2