The atom-bond connectivity (ABC) index is a recently introduced topological index, defined as ABC(G) = ∑ uv∈E(G) √ du+dv−2 dudv , where du (or dv) is the degree the vertex u (or v). The ABC index of benzenoid systems and phenylenes are computed, a simple relation is established between the atom-bond connectivity index of a phenylene and the corresponding hexagonal squeeze in this paper. Mathema...

Bis-iminophosphoranes containing various types of linkers between two R3P==N moieties were electrochemically oxidized at controlled potential in situ in the electron spin resonance (ESR) cavity. For linkers constituted of phenylenes, conjugated phenylenes or merely a dicyanoethylenic bond, this oxidation led to well-resolved ESR spectra which were characterized by their g values and by their 1H...

The geometric-arithmetic index of graph G is defined as GA(G) = ∑ uv∈E(G) 2 √ dudv du+dv , du (or dv) is the degree the vertex u (or v). The GA index of benzenoid systems and phenylenes are computed, a simple relation is established between the geometric-arithmetic of a phenylene and the corresponding hexagonal squeeze in this paper. Mathematics Subject Classification: 05C05, 05C12

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...

A new parameter, related to and easily determined from the structure of a benzenoid system and that of a phenylene – the number of inlets (r) – is introduced. The connectivity (Randi}) index of both benzenoid systems and phenylenes is then shown to depend solely on the number of vertices and on r. A simple relation is established between the connectivity index of a phenylene and of the correspo...

The synthesis of new heterocyclic oligo(phenylene) analogues based on soluble, nonaggregating 1,2-diazines is reported. Improved palladium-catalyzed reductive coupling methods were developed to allow for the preparation of large quantities of iptycene-derived bipyridazines and biphthalazines, and the controlled synthesis of well-defined oligomers up to sexipyridazine. Crystallographic, spectros...

The cut method proved to be utmost useful to obtain fast algorithms and closed formulas for classical distance based invariants of graphs isometrically embeddable into hypercubes. These graphs are known as partial cubes and in particular contain numerous chemically important graphs such as trees, benzenoid graphs, and phenylenes. It is proved that the cut method can be used to compute an arbitr...