Topological indices and graph polynomials of some macrocyclic belt-shaped molecules

Abstract

Two classes of molecular graphs are studied, denoted by H_g,n and M_g,n, corresponding to macrocyclic belt-shaped molecules of Hückel and Möbius type. Both H_g,n and M_g,n consist of a chain of n linearly fused cycles of size 2g; the ends of this chain are joined, forming macrocycles. This joining can be done with a 180° twist of the chain (resulting in the Möbius isomer M_g,n) or without twist (resulting in the Hückel isomer H_g,n). Certain regularities are established for the Z-counting and independence polynomials of H_g,n and M_g,n, as well as for their topological indices. The results obtained generalize findings previously reported for the cyclic ladders (H_2,n and M_2,n).