Dataset complementary prism networks

The complementary prism of G , denoted by G G ¯ , is the graph obtained from the disjoint union of G and G ¯ by adding edges between the corresponding vertices of G and G ¯ . Up to date, the progress of experimental research around complementary prisms is limited by the unavailability of publicly available instances that could be used to run extensive experiments and to compare the performance on different topological index solutions and its bounds. For this reason, we decided to make publicly available 435 instances of type G G ¯ randomly generated, with increasing network size (from 12 to 1948 nodes). The dataset presents instances of Complementary Prism Networks suitable to measure the Wiener Index and Generalized Wiener Index and the value of these indices for these instances. In addition, are presented the value of some lower and upper bounds proposed in the literature for these indices and their error with respect to the value of the index.

Synthesis, photoinduced amination and topological indices of novel porphyrin dyads

Transition-metal-catalyzed homo and hetero coupling is a rapidly growing area of research. This work refers to the nickel-catalyzed photoinduced amination study of [Formula: see text]-bromotetraarylporphyrin and its Ni(II), Zn(II) and Cu(II) complexes. The selective mono [Formula: see text]-bromination of 5,10,15,20-tetrakis(4[Formula: see text]-isopropylphenyl)porphyrin was achieved with [Formula: see text]-bromosuccinimide. Under similar conditions, [Formula: see text]-bromination of Ni(II), Zn(II) and Cu(II) complexes of 5,10,15,20-tetrakis(4[Formula: see text]-isopropylphenyl)porphyrin successfully afforded the corresponding 2-bromometalloporphyrins. The [Formula: see text]-bromoporphyrin/metalloporphyrins were coupled with three different amines through the creation of the C–N bond by using an economical and air-tolerant photoactive catalyst (NiBr[Formula: see text] · 3H2O) at room temperature under 365 nm radiations. Nickel-catalyzed amination yields are compared with the traditional Buchwald–Hartwig amination yields. Due to the low operational cost, photoinduced nickel-catalyzed C–N couplings were found to be more economical than the Buchwald–Hartwig amination procedure, although the latter afforded higher yields. The nickel-catalyzed photoamination reaction was also extended for the one-pot synthesis of pyridine-3,5-diamine bridged porphyrin dyad. The intramolecular cyclization of the pyridine-3,5-diamine-bridged porphyrin dyad afforded a novel quinolino-fused porphyrin dyad. Degree- and distance-based topological indices of the newly synthesized porphyrins were calculated and correlated with their molar refractivity. All newly synthesized porphyrins are characterized by UV-vis, FTIR, 1H NMR, elemental analysis and mass spectrometry.

New Bounds for Topological Indices on Trees through Generalized Methods

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.

Design of topological indices: computer-oriented approach

A novel method is suggested for constructing topological indices (TIs) of molecular graphs which models human logic. This method is described in terms of a block scheme, consisting of the mutually connected elementary blocks. In each block the simple transformations of a molecular graph are fulfilled. A variant of the transformation is selected from the list of possible variants. Every TI is obtained as a result of the sequential execution of a number of operations, corresponding to some 'walk' on the block scheme. This walk can be selected both randomly and by the investigator. The suggested method can serve as a basis for the development of the respective computer program which may be used for the automatic construction of any number of TIs of differing nature. By this process one can also obtain the TIs that are unlikely to be constructed manually, due to their complexity. The set of obtained TIs may be used for building the structure-property models. In the case of an unsatisfactory result the obtained set of TIs may be changed using the described generator of TIs. A number of examples of application of the suggested approach for the building QSAR/QSPR models is given.

A novel definition of the overall hyper-wiener index for unsaturated hydrocarbons

By replacing the distances between pairs of vertices with the relative distances, we define a novel overall hyper-Wiener index (NOR); the novel overall hyper-Wiener index extends the usefulness of the hyper-Wiener index and the overall hyper-Wiener index to unsaturated hydrocarbons.

The Wiener distance matrix for acyclic compounds and polymers

The relationship between the Wiener indices and the topological structures of alkanes is analyzed. The expressions for the Wiener distances between elements of these structures are derived, and the distance matrix is constructed for them; this matrix is naturally called the Wiener distance matrix. The expressions for the Wiener indices of polymers with units of arbitrary structure are obtained.

The extended hyper-Wiener index

According to the definition of molecular connectivity and the definition of a hyper-Wiener index, a novel set of hyper-Wiener indexes (Rn, mRn) are defined and are named the extended hyper-Wiener indexes. Where n = 1, 2, 3, 4,... represents the type of subgraph units and is the number of endmost atoms of the subgraph unit, m is the number of atoms of the subgraph unit. Here n = 1 means the subgraph unit is an atom, n = 2 means the subgraph units are straight-line combinations of m atoms (m = 2, 3, 4, 5, 6,...), and n = 3 means the subgraph units are Y types of combinations of m atoms (m = 4, 5, 6, 7, 8,...), and so on. The potential usefulness of the extended hyper-Wiener index in QSAR and (or) QSPR is evaluated by its correlation with a number of C3–C8 alkanes and by a favorable comparison with models based on the molecular connectivity index and the overall Wiener index. To verify the robustness and the predictive ability of the models, a cross-validation procedure, leave-one-out, and a random test were also performed. The results show that the extended hyper-Wiener indexes examined demonstrate a good potential for QSAR and QSPR studies. Considerably better statistics are obtained when extending the hyper-Wiener index to the extended hyper-Wiener index. The extended hyper-Wiener indexes provided statistical results as good as the molecular connectivity indexes and the overall Wiener index in all models, and the standard deviations provided by these three sets of indexes are rather close. Moreover, this method may provide a better way to apply the Wiener number and the hyper-Wiener index to the system of unsaturated hydrocarbons and organic compounds, including heteroatoms, according to the method of the molecular connectivity index. This can extend the usefulness of the Wiener number and hyper-Wiener index and can make them a kind of widely used topological index in practice.Key words: hyper-Wiener index (R), extended hyper-Wiener index, molecular connectivity index.

Polynomial expressions for the hyper-Wiener index of extended hydrocarbon networks

General expressions are derived for the hyper-Wiener index (WW) for several series of hydrocarbons, both benzenoid and non-benzenoid, including some two-dimensional networks. Indeed, such expressions were found for all but one series studied. Methods are also described for eliminating the register overflow problem that besets computer-based approaches to calculating WW for large structures by means of the distance matrix.

QSAR for boiling points of "small" sulfides. Are the "high-quality structure-property-activity regressions" the real high quality QSAR models?

Our investigation was motivated by a recent paper concerning "high-quality structure-property-activity regressions" (J. Chem. Inf. Comput. Sci. 2000, 40, 899-905) for boiling points of small sulfides using variable connectivity indices. We performed QSAR study of the same data set using a logically preselected solvation index and obtained a very good one-parameter regression. The structures of the whole possible set of small sulfides (C2-C6) were generated and the statistics were proven by real prediction using an external test set of sulfides. The variants of extended prediction with extrapolated data and QSAR using an expanded training set were also performed, and all these data also revealed the preference of the solvation index. A general problem of descriptive vs predictive QSAR is discussed.

The overall Wiener index--a new tool for characterization of molecular topology

Recently, the concept of overall connectivity of a graph G, TC(G), was introduced as the sum of vertex degrees of all subgraphs of G. The approach of more detailed characterization of molecular topology by accounting for all substructures is extended here to the concept of overall distance OW(G) of a graph G, defined as the sum of distances in all subgraphs of G, as well as the sum of eth-order terms, (e)OW(G), with e being the number of edges in the subgraph. Analytical expressions are presented for OW(G) of several basic classes of graphs. The overall distance is analyzed as a measure of topological complexity in acyclic and cyclic structures. The potential usefulness of the components of this generalized Wiener index in QSPR/QSAR is evaluated by its correlation with a number of properties of C3-C8 alkanes and by a favorable comparison with models based on molecular connectivity indices.

Relation between distance-based topological indices

The pi-index of the line graph of the molecular graph of an alkane is shown to be related to the pi, Harary, and reciprocal Wiener indices of that alkane. Thus a mathematical relation between several distance-based topological indices is obtained.

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.