• 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

Topological indices are numerical quantities associated with the molecular graph of a chemical structure. These used to predict various properties structures. Imbalance-based analysis is an advanced technique for compounds irregular characteristics. The graphs zigzag benzenoid systems <m...

An algorithm for the calculation of the hyper-Wiener index (WW) of benzenoid hydrocarbons (both cata- and pericondensed) is described, based on the consideration of pairs of elementary cuts of the corresponding benzenoid graph B. A pair of elementary cuts partitions the vertices of B into four classes. WW is expressed as a sum of terms of the form n11n22 + n12n21, each associated with a pair of...

The phenomenon of resonance amongst a set of different classical chemical structures entails at an elementary level the enumeration of these resonance structures, corresponding (in benzenoid molecules) to perfect matchings of the underlying molecular (n-network) graph. This enumeration is analytically performed here for the finite-sized elemental benzenoid graphs corresponding to hexagonal cove...

An efficient algorithm leading to the Fries canonical structure is presented for benzenoid hydrocarbons. This is a purely topological approach, which is based on adjacency matrices and the Hadamard procedure of matrix multiplication. The idea is presented for naphthalene, as an example. The Fries canonical-structures are also derived for anthracene, coronene, triphenylene, phenanthrene, benz[a]...

Clar's aromatic sextet theory provides a good means to describe the aromaticity of benzenoid hydrocarbons, which was mainly based on experimental observations. Clar defined sextet pattern and Clar number of benzenoid hydrocarbons, and he observed that for isomeric benzenoid hydrocarbons, when Clar number increases the absorption bands shift to shorter wavelength, and the stability of these isom...