Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the linear programming relaxation always yields integral solutions. We prove this conjecture showing...

Distance properties of molecular graphs form an important topic in chemical graph theory.1 To justify this statement just recall the famous Wiener index which is also known as the Wiener number. This index is the first2 but also one of the most important topological indices of chemical graphs. Its research is still very active; see recent reviews3,4 and several new results in a volume5 dedicate...

• The Tutte polynomials of fan-like graphs are obtained via generating functions. As applications, polynomials, in particular, the number spanning trees, two kinds benzenoid systems, i.e. pyrene chains and triphenylene chains, obtained. We study computation obtain expressions their

Gutman proposed a new alternative interpretation of vertex-degree-based topological index, called Sombor index. It is defined via the term . In this paper, we determine explicit expressions index for line and total graphs several pericondensed benzenoid hydrocarbons.

The aim of this paper is to investigate resonance graphs 2- connected outerplane bipartite graphs, which include various families molecular graphs. Firstly, we present an algorithm for a binary coding perfect matchings these Further, with isomorphic are considered. In particular, it shown that if two evenly homeomorphic, then its isomorphic. Moreover, prove any 2-connected graph G there exists ...

A naturally occurring enynyl-benzenoid, benzocamphorin F (1), from the edible fungus Taiwanofungus camphoratus (Antrodia camphorata) was characterized by comprehensive spectral analysis. It displays anti-inflammatory bioactivity and is valuable for further biological studies. The present study is the first total synthesis of benzocamphorin F and the developed strategy described is a more effici...

Two-dimensional arrays consisting of strongly subspectral molecular graphs and formula periodic tables for polycyclic aromatic hydrocarbons are briefly reviewed. New two-dimensional arrays for free-radical benzenoid hydrocarbons are presented with general analytical expressions for counting their number of resonance structures (SC). The structural origin of the coefficients to these analytical ...

A new and facile synthesis of 2-thioxoquinazolin-4-ones by introducing a benzenoid system in the pyrimidine moiety by reacting ethoxymethylene derivatives of 1,3-diarylthiobarbituric acids (DTBA) with active methylene compounds, such as malononitrile and ethyl cyanoacetate, in presence of ZnCl₂ has been developed.

It is shown that the number of Clar formulas of a Kekuléan benzenoid system B is equal to the number of subgraphs of the resonance graph of B isomorphic to the Cl(B)-dimensional hypercube, where Cl(B) is the Clar number of B.