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...

1031 Vertex-degree-based molecular structure descriptors of benzenoid systems and phenylenes IVAN GUTMAN* and BORIS FURTULA** Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia (Received 12 December 2011) Abstract. Several recently published papers report expressions for various vertex-degree-based molecular structure descriptors of benzenoid systems and phenyl...

A large number of local aromaticity indices for the benzenoid rings in polyaromatic hydrocarbons is computed. The results are interpreted, supporting Clar's hypothesis, and mutual correlations are investigated. It is shown that there are good correlations between all indices that strictly allow comparing benzenoid character. Poor correlations are found with NICS. A rationale is offered, yieldin...

T This paper analyzes different pricing strategies in a two-echelon supply chain including one supplier and two retailers. The supplier and the retailers face random yield and random demand, respectively. Moreover, coordination or non-coordination of retailers in receiving the discount is investigated. Game theory is used to model and analyze the problems. The supplier as a leader of Stackelbe...

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then EE = n ∑ i=1 eλi . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√ 2m/n ) +a2, where a1 ≈ 1.098 and a2 =−0.64 are empirically determined fitt...

It has been shown by TE NIJENHUIS and BERENDS2 that the benzenoid (or better: o-quinoid) subnucleus of alloxazines can be attacked photochemically. We found that with flavins the reaction products bear a hydroxyl group either in the 6 or in the 9 position of the benzenoid nucleus. The reactive species is the protonated flavin, the rate of the reaction has an optimum at pH 0 — 1. At still lower ...

In this note we present some new results on distances in benzenoids. An algorithm is presented which, for a given benzenoid system G bounded by a simple circuit 2 with n vertices, computes the Wiener index of G in O(n) time. Also we show that benzenoid systems have a convenient dismantling scheme, which can be derived by applying breadth-first search to their dual graphs. Our last result deals ...