Computer generation of generalized Wheland polynomials

Abstract

Generalized Wheland polynomials enumerate the valence structures of different degrees of excitation. As such they are structural invariants which may be of interest in discussions of similarities and differences among unsaturated compounds. Brute force enumeration of valence structures is already impractical for graphs having n = 10 vertices (e.g. naphthalene C 10H 8). Here we outline a computer program which enumerates valence structures of any degree of excitation. The results are illustrated on linear chains, cycles, and smaller benzenoid systems. Some properties of the derived polynomials are discussed. The recursive relation for the generalized Wheland polynomials is given. Because of the nonpolynomial character of the problem the computer application is practical only for graphs having n = 16 and less vertices.