Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

Fullerene is a cage-like carbon allotrope admitting vast range of applications. Some the important fullerenes are C54,C58,C60,C70,C74,C76,C78,C80C82,C84,C86,C90. The physical properties can be exhibited using degree-based topological indices. sum based geometric arithmetic index significant in this manner. atomic bond connectivity, Randic, first and second Zagreb indices well known We have dete...

All the drugs used as analgesic agent have some systemic side effects. For the researchers, the prospects of overcoming the side effects of a drug, achieving an effect at a much lower dose is very attractive. Modification of the structure of a known drug is one way to develop new drugs. For this purpose, we have optimized the pyrimidobenzimidazole derivatives using molecular modeling studies. Q...

We introduce a partial order on the collection of chemical trees based on tree transformations. This partial order is tightly related to the Randić connectivity index χ. Its analysis provides new structural information about the behavior of χ. As an illustration of the approach presented, we give a different and more structural view of some known results about the first values of χ on the colle...

In this research paper, we will compute the topological indices (degree based) such as ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, hyper-Gourava general Randic´ index R γ G ,</mo...

Let G be a simple connected graph and t be a given real number. The zero-order general Randić index αt(G) of G is defined as ∑ v∈V (G) d(v) t , where d(v) denotes the degree of v. In this paper, for any t , we characterize the graphs with the greatest and the smallest αt within two subclasses of connected unicyclic graphs on n vertices, namely, unicyclic graphs with k pendant vertices and unicy...

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

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...

BACKGROUND Synthesizing and characterizing aptamers with high affinity and specificity have been extensively carried out for analytical and biomedical applications. Few publications can be found that describe structure-activity relationships (SARs) of candidate aptamer sequences. METHODOLOGY This paper reports pattern recognition with support vector machine (SVM) classification techniques for...