Computing the connectivity indices of α- and β-cyclodextrins

Graph theory was successfully applied in developing a relationship between chemical structure and biological activity. The m-connectivity index of a graph G is defined to be ^mχ(G) = Σ_v1V2⋯Vm+1(d_v1d_V2⋯d_Vm+1)-1/2 where v. v. ⋯v_m. . runs over all paths of length m in G and d_i is the degree of vertex v_i. Cyclodextrins are a family of compounds widely used in food, pharmaceutical, and chemical industries. In this paper we give explicit formulas for computing the first-, second-, and third-order connectivity indices of the molecular graphs of two classes of cyclodextrins, namely α-cyclodextrin and β-cyclodextrin. These formulas are helpful in the study of the relationship between the structure and activity of these cyclodextrins.