Kekulé structures belong to the classical concepts of theoretical chemistry of polycyclic conjugated molecules and, in particular, of benzenoid hydrocarbons [1 – 3]. Nevertheless, it was only quite recently recognized [4] that in addition to the standard representation of a Kekulé structure (in which the locations of the double bonds are indicated), also an “algebraic” representation is possibl...

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...

The algebraic Kekulé structure of a finite catacondensed benzenoid graph with h hexagons is described by a binary code of length h. The procedure can be reversed, any (algebraic) Kekulé structure can be recovered from its binary code. c © 2007 Elsevier Ltd. All rights reserved.

We investigate the role of Kekulé and non-Kekulé structures in the radical character of alternant polycyclic aromatic hydrocarbons (PAHs) using thermally-assisted-occupation density functional theory (TAO-DFT), an efficient electronic structure method for the study of large ground-state systems with strong static correlation effects. Our results reveal that the studies of Kekulé and non-Kekulé ...

An algorithm is described by means of which the Kekulé structures of a catacondensed benzenoid molecule (with h hexagons) are transformed into binary codes (of length h). By this, computer-aided manipulations with, and memory-storage of Kekulé structures are much facilitated. Any Kekulé structure can easily be recovered from its binary code.

Anti-Kekulé problem is a concept of chemical graph theory precluding the Kekulé structure of molecules. Matching preclusion and conditional matching preclusion were proposed as measures of robustness in the event of edge failure in interconnection networks. It is known that matching preclusion problem on bipartite graphs is NP-complete. In this paper, we mainly prove that anti-Kekulé problem on...

The configurations of single and double bonds in polycyclic hydrocarbons are abstracted as Kekulé states of graphs. Sending a socalled soliton over an open channel between ports (external nodes) of the graph changes the Kekulé state and therewith the set of open channels in the graph. This switching behaviour is proposed as a basis for molecular computation. The proposal is highly speculative b...

a fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons.the clar number of a fullerene is the maximum size of sextet patterns, the sets of disjointhexagons which are all m-alternating for a kekulé structure m of f. an exact formula of clarnumber of some fullerene graphs and a class of carbon nanocones are obtained in this paper.

Fullerene graphs are trivalent plane graphs with only hexagonal and pentagonal faces. They are often used to model large carbon molecules: each vertex represents a carbon atom and the edges represent chemical bonds. A totally symmetric Kekulé structure in a fullerene graph is a set of independent edges which is fixed by all symmetries of the fullerene and molecules with totally symmetric Kekulé...

(Received May 2, 2012) Graph theoretic fullerenes are designed to model large carbon molecules: each vertex represents a carbon atom and the edges represent chemical bonds. A totally symmetric Kekulé structure in a fullerene is a set of independent edges which is fixed by all symmetries of the fullerene. It was suggested in a paper by S.J.Austin, J.Baker, P.W.Fowler, D.E.Manolopoulos and in a p...