A recently published paper [T. Došlić, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by u...

The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, the d-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the resonance graphs of a subclass of the catacon...

The concept of numerical Kekulé structures is used for coding and ordering geometrical (standard) Kekulé structures of several classes of polycyclic conjugated molecules: catacondensed, pericondensed, and fully arenoid benzenoid hydrocarbons, thioarenoids, and [N]phenylenes. It is pointed out that the numerical Kekulé structures can be obtained for any class of polycyclic conjugated systems tha...

After an introduction on the history of polycyclic aromatic compounds, recent advances in the theory of benzenoids are briefly reviewed. Then using systems with 4, 5, or 6 benzenoid rings for illustration, the partition of the P π-electrons among the rings of the benzenoid is presented, followed by a different way of examining the distribution of these π-electrons which is called the signature ...

The Fibonacci dimension fdim(G) of a graph G was introduced in [7] as the smallest integer d such that G admits an isometric embedding into Qd, the d-dimensional Fibonacci cube. A somewhat new combinatorial characterization of the Fibonacci dimension is given, which enables more comfortable proofs of some previously known results. In the second part of the paper the Fibonacci dimension of the r...

Recent experimental methods have made it possible to synthesize very large benzenoid molecules, sometimes referred to as “graphenes”.1–3 These have found unprecedented applications as organic materials for electronic and optoelectronic devices.2,3 As large benzenoid systems have countless possible isomers,4–6 it is a task of theoretical chemistry to help indicate those species that may possess ...

1031 Vertex-degree-based molecular structure descriptors of benzenoid systems and phenylenes IVAN GUTMAN* and BORIS FURTULA** Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia (Received 12 December 2011) Abstract. Several recently published papers report expressions for various vertex-degree-based molecular structure descriptors of benzenoid systems and phenyl...