Floral volatile benzenoid/phenylpropanoid (FVBP) biosynthesis is a complex and coordinate cellular process executed by petal limb cells of a Petunia×hybrida cv. 'Mitchell Diploid' (MD) plant. In MD flowers, the majority of benzenoid volatile compounds are derived from a core phenylpropanoid pathway intermediate by a coenzyme A (CoA) dependent, β-oxidative scheme. Metabolic flux analysis, revers...

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...

It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of G is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, k-cycle resonant graphs, Discrete Math. 135 (1994) 113-120] that a hexagonal system is 1-cycle resonant if and only if it is...

It is shown that the vertices of benzenoid systems admit a labeling which reflects their distance relations. To every vertex of a molecular graph of a benzenoid hydrocarbon a sequence of zeros and ones (a binary number) can be associated, such that the number of positions in which these sequences differ is equal to the graph-theoretic vertex distance. It is shown by an example that such labelin...

The importance of caterpillar trees in the topological theory of benzenoid systems lies in the following. Let B be a non-branched cata-condensed benzenoid hydrocarbon (that is a hydrocarbon containing linearly and angularly condensed rings). If we associate a symbol L to each linearly condensed ring (and also to the two terminal ones) and a symbol A to each angularly condensed ring, then the so...

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...

The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent if their symmetric difference forms the edge set of a hexagon of B . A family P of pair-wise disjoint hexagons of a benzenoid graph B is resonant in B if B−P contains at least one perfect matching, or if B − P is empty. It is proven that there exists a surjective map ...

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...