THE THETA Θ(G,X) POLYNOMIAL OF AN INFINITE FAMILY OF THE LINEAR PARALLELOGRAM P(N,M)

The Omega polynomial was defined by M.V. Diudea as Ω(G,x)=Σc m(G,c)mc, where the number of edges co-distant with e is denoted by c and m(G,c) is the number of its repeatation. One can obtain the Θ polynomial by inserting the coefficient c in the Omega polynomial. Then the Theta index will be the first derivative of the Theta Θ(G,x) polynomialevaluated at x=1.
In the present study, compute the Theta Θ(G,x) polynomial and the Theta Θ(G) index of an infinite family of the linear parallelogram P(n,m) of benzenoid graph is computed for the first time.