The first time I heard about the “Kekulé Riddle” was during a lecture that Dr. Alfred Bader, the founder of the Aldrich Chemical Company (now Sigma-Aldrich), gave at the Department of Chemistry and Biochemistry of the University of Maryland, College Park. Dr. Bader presented evidence that when the German chemist Friedrich August Kekulé published his paper on the benzene ring, he had already see...

We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekulé distortions (i.e., Kekulé-O, Kekulé-Y and Kekulé-M). On one hand, we numerically show visualized evolution process quasiparticles; while on other analytically obtain centroid trajectory quasiparticles, both them agree well each other. The results reveal that relativistic Zitterbewegung ...

We explore the relationship between Kekulé structures and maximum face independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. For the class of leap-frog fullerenes, we show that a maximum face independence set corresponds to a Kekulé structure with a maximum number of benzene rings and may be constructed by partitioning the pentagonal faces into pairs and 3...

At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged ...

Perfect matchings in chemical graphs correspond to Kekulé structures underlying structure, which play an important role the analysis of resonance energy and stability certain compounds. In 2007, Vukičević Trinajstić introduced concept anti-Kekulé number be smallest edges that have removed from a graph such it remains connected but without any perfect matching. Thereafter, this parameter attract...

The molecular structure of any system may be unambiguously described by its adjacency matrix, A, in which bonds are assigned entry a(ij) = 1 and non-bonded pairs of atoms entry a(ij) = 0. For π-electron-containing conjugated hydrocarbons, this matrix may be modified in order to represent one of the possible Kekulé structures by assigning entry 1 to double bonds and entry 0 to single bonds, lead...

The anti-Kekulé number is the smallest number of edges that must be removed from a connected graph with a perfect matching so that the graph remains connected, but has no perfect matching. In this paper the values of the Anti-Kekulé numbers of the infinite triangular, rectangular and hexagonal grids are found, and they are, respectively, 9, 6 and 4.

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjuga...

G. Clar 6n Rule versus Hückel 4n + 2 Rule 3464 H. Hydrocarbons versus Heteroatomic Systems 3465 IV. Hidden Treasures of Kekulé Valence Structures 3466 A. Conjugated Circuits 3467 B. Innate Degree of Freedom 3470 C. Clar Structures 3472 V. Graph Theoretical Approach to Chemical Structure 3473 A. Metric 3473 B. Chemical Graphs 3473 C. Isospectral Graphs 3473 D. Embedded Graphs 3475 E. Partial Ord...

Fluoranthenes are polycyclic conjugated molecules consisting of two benzenoid fragments, connected by two carbon–carbon bonds so as to form a five-membered ring. Fluoranthenes possessing Kekulé structures are classified into three types, depending on the nature of the two carbon–carbon bonds connecting the two benzenoid fragments. Either both these bonds are essentially single (i. e., single in...