TheWiener polarity indexWp(G) of a graphG of order n is the number of unordered pairs of vertices u and v of G such that the distance dG(u, v) between u and v is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and C4 nanotubes and nanotori are computed. AMS Mathematics Subj...

Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely...

The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb latt...

published in Aduance ACS Abstracts, February 15, 1994. 0095-233819411634-0421$04.50/0 Fueled by the intense activity in fullerene chemistry and intrinsically interesting geometrical and topological features of fullerenes, several studies have focused on the fascinating mathematical properties of fullerenes. These studies included graph theoretical computations of the characteristic polynomials,...

In this study, paraphenylenediamine was first bonded to the fullerene and was optimized geometrically by Using the quantum chemistry methods. paraphenylenediamine was examined in the isolated state and in the fullerene-bonded state via carbon atoms. In the theoretical research, the simulation was done by the Gauss View software. Then, the bonding orbital calculation was done by using the NBO me...

The antitumor activity of pristine C60 fullerene aqueous solution (C60FAS) compared to 5-fluorouracil (5-FU) and pyrrole derivative 1-(4-Cl-benzyl)-3-Cl-4-(CF3-fenylamino)-1H-pyrrol-2.5-dione (MI-1) cytostatic drugs was investigated and analyzed in detail using the model of colorectal cancer induced by 1.2-dimethylhydrazine (DMH) in rats. The number, size, and location of the tumors were measur...

Classification of chemical entities is generally based on identifying the interesting parts and properties of the molecules. However, classes of chemical entities which are highly symmetrical and which contain large numbers of homogeneous parts (such as carbon atoms) are not straightforwardly classified in this fashion. One such class of molecules is the recently developed fullerene family, dis...

Coxeter’s classification of the highly symmetric geodesic domes (and, by duality, the highly symmetric fullerenes) is extended to a classification scheme for all geodesic domes and fullerenes. Each geodesic dome is characterized by its signature: a plane graph on twelve vertices with labeled angles and edges. In the case of the Coxeter geodesic domes, the plane graph is the icosahedron, all ang...

Fullerene epoxides, C₆₀O(n), having epoxide groups directly attached to the fullerene cage, constitute an interesting class of fullerene derivatives. In particular, the chemical transformations of fullerene epoxides are expected to play an important role in the development of functionalized fullerenes. This is because such transformations can readily afford a variety of mono- or polyfunctionali...