Localized molecular orbitals for n-systems of conjugated polycyclic hydrocarbons have been calculated using both intrinsic and external localization criteria relying only on molecular topology. For benzenoid aromatic compounds the intrinsic localized molecular orbital arrangement can always be associated to the Kekule structure of maximal Kekule index value. However hydrocarbons containing four...

Harary’s & Randić’s ideas of “forcing” & “freedom” involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with il...

Following the recent realization of an artificial version of graphene in the electronic surface states of copper with judiciously placed carbon monoxide molecules inducing the honeycomb lattice symmetry [Gomes et al., Nature (London) 483, 306 (2012)], we demonstrate that these can be used to realize a vortex in a Kekule texture of the honeycomb lattice. The Kekule texture is mathematically anal...

The enumeration of Kekule structures has fasci­ nated several researchers since the first systematic studies of benzenoids in terms of graph theory [1-9] , Apart from the recognized importance of Kekule structures in organic and physical chemistry they also have purely mathematical interest. Refer­ ence is made to a recent article in the present jo u r ­ nal [10] along with the bibliography the...

Two empirical rules are formulated for the topological resonance energy (TRE) of benzenoid hydrocarbons: (a) TRE is roughly linear function of the number of Kekule structures, and (b) in a homologous series containing a linear polyacene fragment, TRE is a linear function of the length of this fragment. In certain cases, however, the TRE model leads to incorrect predictions. There exist pairs of...

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...

Among the vast number of polyhex graphs corresponding to polycyclic aromatic hydrocarbons several graphs are known to have a vexing property with respect to the perfect matching, or Kekulć structure counting problem." Examples are 12 and 23, which have the same number of starred I_I and unstarred IO I atoms but have no Kekule structure (See the left half of Figure 1). Further, both of them have...