Applications of Multidimensional Space of Mathematical Molecular Descriptors in Large-Scale Bioactivity and Toxicity Prediction- Applications to Prediction of Mutagenicity and Blood-Brain Barrier Entry of Chemicals

In this chapter, we review our QSAR research in the prediction of toxicities, bioactivities and properties of chemicals using computed mathematical descriptors. Robust statistical methods have been used to develop high quality predictive quantitative structure-activity relationship (QSAR) models for the prediction of mutagenicity and BBB (blood-brain barrier) entry of two large and diverse sets chemicals. This work is licensed under a Creative Commons Attribution 4.0 International License

Some properties on the lexicographic product of graphs obtained by monogenic semigroups

In (Das et al. in J. Inequal. Appl. 2013:44, 2013), a new graph Gamma (S-M) on monogenic semigroups S-M (with zero) having elements {0, x, x(2), x(3),..., x(n)} was recently defined. The vertices are the non-zero elements x, x(2), x(3),..., x(n) and, for 1 <= i, j <= n, any two distinct vertices x(i) and x(j) are adjacent if x(i)x(j) = 0 in S-M. As a continuing study, in an unpublished work, some well-known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Gamma (S-M) were investigated by the same authors of this paper. In the light of the above references, our main aim in this paper is to extend these studies to the lexicographic product over Gamma (S-M). In detail, we investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the lexicographic product of any two (not necessarily different) graphs Gamma (S-M(1)) and Gamma (S-M(2)).Selçuk ÜniversitesiSungkyunkwan University (BK21

Mathematical Properties of Molecular Descriptors Based on Distances

A survey of a number of molecular descriptors based on distance matrices and distance eigenvalues is given. The following distance matrices are considered: the standard distance matrix, the reverse distance matrix, the complementary distance matrix, the resistance-distance matrix, the detour matrix, the reciprocal distance matrix, the reciprocal reverse Wiener matrix and the reciprocal complementary distance matrix. Mathematical properties are discussed for the following molecular descriptors with a special emphasis on their upper and lower bounds: the reverse Wiener index, the Harary index, the reciprocal reverse Wiener index, the reciprocal complementary Wiener index, the Kirchhoff index, the detour index, the Balaban index, the reciprocal Balaban index, the reverse Balaban index and the largest eigenvalues of distance matrices. This set of molecular descriptors found considerable use in QSPR and QSAR

The Laplacian-energy like of graphs

AbstractAssume that μ1,μ2,…,μn are eigenvalues of the Laplacian matrix of a graph G. The Laplacian-energy like of G, is defined as follows: LEL(G)=∑i=1nμi. In this note, we give upper bounds for LEL(G) in terms of connectivity or chromatic number and characterize the corresponding extremal graphs

Graphs and networks theory

This chapter discusses graphs and networks theory

WIENER INDEX OF SOME ACYCLIC GRAPHS

In the field of chemical graph theory, a topological index (a.k.a.connectivity index)is a type of molecular descriptor that is calculated based on the molecular graph of a chemical compound[5]. In this thesis, we have studied one of the well-known topological indices called Wiener. It is obtained by adding all the geodesic distances (or shortest paths) of the graph. As the number of vertices grows for anygraph, so does the Wiener number of that graph. We determine the Wiener values associated with several graphs, as functions of the number of vertices. We found that these infinite integer sequences have general formulae which include summations of triangular numbers. Further, we introduced new classes of trees and derived newinfinite integer sequences that are not available in the largest online encyclopedia of integer sequences