Graph representation of organic molecules Cayley's plerograms vs. his kenograms

Abstract

The structure of an organic molecule can be represented by two types of molecular graphs, which, following Cayley's terminology, are referred to as a plerogram, Pl, (in which each atom is represented by a vertex) and a kenogram, Ke, (in which the hydrogen atoms are disregarded). In contemporary chemical graph theory almost all considerations are based on kenograms. We show that, in the case of alkanes this neglect of plerograms is partially justified. Namely, for TI being any of the numerous recently studied distance-based topological indices, there exists a good linear correlation between TI(Pl) and TI(Ke). If TI is the Wiener index, W, then an exact relation applies: W(Pl) = 9W(Ke) + (3n + 1)², where n is the number of carbon atoms.