CVNET SOFTWARE PROGRAM AND GENERATED STRUCTURES

Abstract: A map M is a combinatorial representation of a graph embedded on a surface and creates a tessellation on that surface. The map operations are topological transformations of a given map. A computer program, CVNET, was made for generating maps or coverings representing fullerenes/ hyper structures, by map operations. In this paper are presented algorithms for map operations, which analyze the original graph and then generate the new ones. Some examples of generated objects by map operations are illustrated at the end

Generalized Operations on Maps

A map M is a combinatorial representation of a closed surface. Convex polyhedra, starting from the Platonic solids and going to spherical fullerenes, can be operated to obtain new objects, with a larger number of vertices and various tiling. Three composite map operations: leapfrog, chamfering and capra, play a central role in the fullerenes construction and their electronic properties. Generalization of the above operations leads to a series of transformations, characterized by distinct, successive pairs in the Goldberg multiplication formula m(a,b). Parents and products of most representative operations are illustrated

Wiener Index of Armchair Polyhex Nanotubes

Formulas for calculating the sum of all distances, known as the Wiener index, in the »armchair« nanotubes are given. The same method was applied in the case of »zig-zag« tubes

C70 Dimers – Energetics and Topology

All sp2 peanut-shaped dimeric fullerenes derived from D5h C70 are modeled. Construction of the isomers was monitored by a cyclic permutation of bonds in the linking zone of the two caps resulting from deleting the boundary of a face from the parent C70 fullerene. Local curvature was calculated in terms of both angular defects and strain energy. Topological equivalence classes of the constituent substructures were evaluated by calculating the topological indices of the parent cages, their medials and duals. Detailed network transformation, starting from C70, through sp3 dimer, peanut sp2 dimer, up to the corresponding tubulene is given. Semiempirical calculations showed a monotonic decrease in the heat of formation along the above pathway

Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices.

In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164-168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work

L'Avenir de Bel-Abbès. Journal agricole, commercial, industriel, politique et littéraire paraissant les mercredis et samedis

23 août 18841884/08/23 (A2,N158)-1884/08/23.Appartient à l’ensemble documentaire : Pam