Valencies of Property

Basic topological matrices: the adjacency matrix, A, the distance matrix, D, the Wiener matrix, W, the detour matrix, &Delta, the Szeged matrix, SZu, and the Cluj matrix, CJu, after application of the walk matrix operator, W(M1,M2,M3), result in matrices whose row sums express the product between a local property of a vertex i and its valency. One of the two variants of these valency-property matrices is derived by a simple graphical method. Non-Cramer matrix algebra involved in the walk matrix is exemplified. Relations of the indices, calculated on these matrices, with the well known indices of Schultz and Dobrynin (valency-distance) indices are discussed. Further use of the obtained matrices is suggested

Wiener-Type Topological Indices

A unified approach to the Wiener topological index and its various recent modifications, is presented. Among these modifications particular attention is paid to the Kirchhoff, Harary, Szeged, Cluj and Schultz indices, as well as their numerous variants and generalizations. Relations between these indices are established and methods for their computation described. Correlation of these topological indices with physico-chemical properties of molecules, as well as their mutual correlation are examined

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

Valencies of Property

Basic topological matrices: the adjacency matrix, A, the distance matrix, D, the Wiener matrix, W, the detour matrix, &Delta, the Szeged matrix, SZu, and the Cluj matrix, CJu, after application of the walk matrix operator, W(M1,M2,M3), result in matrices whose row sums express the product between a local property of a vertex i and its valency. One of the two variants of these valency-property matrices is derived by a simple graphical method. Non-Cramer matrix algebra involved in the walk matrix is exemplified. Relations of the indices, calculated on these matrices, with the well known indices of Schultz and Dobrynin (valency-distance) indices are discussed. Further use of the obtained matrices is suggested

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

Balaban Index of an Infinite Class of Dendrimers

The Balaban index of a graph G is the first simple index of very low degeneracy. It is defined as the sum of topological distances from a given atom to any other atoms in a molecule. In this paper the Balaban index of an infinite family of dendrimers is computed. The result can be of interest in molecular data mining, particularly in searching the uniqueness of tested (hyper-branched) molecular graphs