Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index defined as ABC(G)= [formula:see text], in which degree of vertex v denoted by dv . Recently, a new version of atom-bond connectivity (ABC4) index was introduced by M. Ghorbani et.al in 2010 and is defined as ABC4(G)= [fo...

A discriminant analysis model is presented for carcinogenic risk. The data set is obtained from the two-year rodent study FDA/CDER database and was divided into a training set of 1022 organic compounds and an external validation test set of 50 compounds. The model is designed to use as a decision support tool for a defined decision threshold, and is thus a binary discrimination into "high risk"...

let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

This work describes QSAR and SAR studies on the reduction of 27 aromatic nitro compounds by xanthine oxidase using both distance-based topological indices and quantum molecular descriptors along with indicator parameters. The application of a multiple linear regression analysis indicated that a combination of distance-based topological indices with the ad hoc molecular descriptors and the indic...

Drugs and chemical compounds are often modeled as graphs in which the each vertex of the graph expresses an atom of molecule and covalent bounds between atoms are represented by the edges between their corresponding vertices. The topological indicators defined over this molecular graph have been shown to be strongly correlated to various chemical properties of the compounds. In this article, by...

Two new approaches are presented for the calculation of atom and bond parameters for heteroatom-containing molecules used in computing graph theoretic invariants. In the first approach, the atom and bond weights are computed on the basis of relative atomic electronegativity, using carbon as standard. In the second system, the relative covalent radii are used to compute atom and bond weights, ag...

Topological indices are of incredible significance in the field graph theory. Convex polytopes play a significant role both various branches mathematics and also applied areas, most notably linear programming. We have calculated some topological such as atom-bond connectivity index, geometric arithmetic K-Banhatti indices, K-hyper-Banhatti modified from families convex through M-polynomials. Th...

The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABC indices of C4 nanotubes and nanotori are computed. © 2011 Elsevier B.V. All rig...