Cluj-Ilmenau index of hexagonal trapezoid system Tb,a and triangular benzenoid Gn

Mohammad Reza Farahani1*, M. R

Abstract

Let G(V,E) be a connected molecular graph without multiple edges and loops, with the vertex set V(G) and edge set E(G), and vertices/atoms x,yÎV(G) and an edge/bond xyÎE(G). Let m(G,c) be the number of qoc strips of length c (i.e. the number of cut-off edges) in the graph G. The Omega Polynomial Ω(G,x) and the Cluj-Ilmenau index CI(G) for counting qoc strips in G were defined by M.V. Diudea as Ω(G,x)= ( , ) x c Σm G c c and CI(G)=[Ω(G,x)’2- Ω(G,x)’-Ω(G,x)”]x=1, respectively. In this paper, we compute an exact formula of these counting topological polynomial and its index for the Benzenoid molecular graphs “Hexagonal Trapezoid system Tb,a and Triangular Benzenoid Gn”