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...

In plants, benzoic acid (BA) is believed to be synthesized from Phe through shortening of the propyl side chain by two carbons. It is hypothesized that this chain shortening occurs via either a beta-oxidative or non-beta-oxidative pathway. Previous in vivo isotope labeling and metabolic flux analysis of the benzenoid network in petunia (Petunia hybrida) flowers revealed that both pathways yield...

An efficient algorithm leading to the Fries canonical structure is presented for benzenoid hydrocarbons. This is a purely topological approach, which is based on adjacency matrices and the Hadamard procedure of matrix multiplication. The idea is presented for naphthalene, as an example. The Fries canonical-structures are also derived for anthracene, coronene, triphenylene, phenanthrene, benz[a]...

Clar's aromatic sextet theory provides a good means to describe the aromaticity of benzenoid hydrocarbons, which was mainly based on experimental observations. Clar defined sextet pattern and Clar number of benzenoid hydrocarbons, and he observed that for isomeric benzenoid hydrocarbons, when Clar number increases the absorption bands shift to shorter wavelength, and the stability of these isom...

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...

zagreb indices belong to better known and better researched topological indices. weinvestigate here their ability to discriminate among benzenoid graphs and arrive at some quiteunexpected conclusions. along the way we establish tight (and sometimes sharp) lower andupper bounds on various classes of benzenoids.

A Clar set of a benzenoid graph B is a maximum set of independent alternating hexagons over all perfect matchings of B. The Clar number of B, denoted by Cl(B), is the number of hexagons in a Clar set for B. In this paper, we first prove some results on the independence number of subcubic trees to study the Clar number of catacondensed benzenoid graphs. As the main result of the paper we prove a...

While briefly reviewing how the concepts of strictly pericondensed, strain-free, Clar's aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons, new structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids made up o...

Polycyclic aromatic hydrocarbons that we previously called total resonant sextet (TRS) benzenoids are revisited within the framework of recent experimental findings. A benzenoid transformation called leapfrogging generates TRS benzenoids. There are 13, 30, and 114 TRS benzenoid isomers with formulas C72H26, C96H30, and C102H32, respectively. “The leapfrogs of benzenoids are 2-factorable” is a s...