A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes

The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence, the Wiener index of this nanotube is computed

Results of Evolution Supervised by Genetic Algorithms

A series of results of evolution supervised by genetic algorithms with interest to agricultural and horticultural fields are reviewed. New obtained original results from the use of genetic algorithms on structure-activity relationships are reported.Comment: 6 pages, 1 Table, 2 figure

The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research

Wiener polynomial derivatives and some other information and topological indices are investigated with respect to their discriminating power and property correlating ability

Euler Characteristic of Polyhedral Graphs

Euler characteristic is a topological invariant, a number that describes the shape or structure of a topological space, irrespective of the way it is bent. Many operations on topological spaces may be expressed by means of Euler characteristic. Counting polyhedral graph figures is directly related to Euler characteristic. This paper illustrates the Euler characteristic involvement in figure counting of polyhedral graphs designed by operations on maps. This number is also calculated in truncated cubic network and hypercube. Spongy hypercubes are built up by embedding the hypercube in polyhedral graphs, of which figures are calculated combinatorially by a formula that accounts for their spongy character. Euler formula can be useful in chemistry and crystallography to check the consistency of an assumed structure. This work is licensed under a Creative Commons Attribution 4.0 International License

Delta Number, Dd, of Dendrimers

General formulas for the calculation of a novel Wiener-type number, D", ,1 in regular dendrimers are proposed. They are derived on the basis of the novel matrix DL! ,1 by using progressive vertex degrees and orbit numberse as parameters. Relations of D", with the well known Wiener.i\u27 W, and hyper-Wiener,? WW, numbers, and a new relation (based on the Dp matrix-) for estimating WW in dendrimers are also given

Molecular Topology. 14. Molord Algorithm and Real Number Subgraph Invariants

An algorithm, MOLORD, is proposed for defining real number invariants for subgraphs of various sizes in molecular graphs. The algorithm is based on iterative line derivati ves and accounts for heteroatoms by means of their electronegativities. It can be used in topological equivalence perception as well as to provide local and global descriptors for QSPR or QSAR studies. The algorithm is implemented on a TURBO PASCAL, TOPIND program and examplified on a set of selected graphs