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

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

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

Cluj-Tehran Index

Abstract A novel topological index, called Cluj-Tehran CT, is defined on the ground of Shell polynomials. The polynomial coefficients are calculated by means of Shell matrices, built up according to the vertex distance partitions of a graph. Close formulas for calculating the Shell polynomial in case of Cluj matrices and the corresponding Cluj-Tehran CT index in several particular classes of graphs are given

Molecular Topology 22.1 Novel Connectivity Descriptors Based on Walk Degrees

An algorithm for generating novel connectivity topological descriptors, denoted SP (subgraph property), is proposed and exemplified for P being the number of vertices N, walk degree wt\u27e), Randić index X, and Wiener index W. SP indices based on wt\u27e) and x wt\u27e) (Razinger\u27s extension of x index) are tested for correlation with some physico-chemical properties of octane isomers