Vertex degree autocorrelation topological index and its application in QSAR study of organic chemicals

Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2  and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.

Definition and Application of Topological Index Based on Bond Connectivity

Bond connectivity topological index S i based on chemical bonds was defined by using a matrix method.And S i is formed by atomic parameters such as the number of valence electrons,the number of the highest main quantum of atoms and the bonding electrons and bond parameters such as the length of bonds,the electronegativity difference of bonding atoms.The molecular bond connectivity topological index S is composed of S i.The thermodynamic properties of saturated hydrocarbons,unsaturated hydrocarbons,oxygen organic,methane halide and transitional element compounds and the molecular bond connectivity topological index S have an optimal correlative relationship.

New autocorrelation topological indexes and their application in QSAR study

Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.

A Novel Topological Index for the Studies on Structure-Properties of Alkanes

A novel topological index derived from eccentric connectivity index has been proposed. The new topological index and eccentric connectivity index were correlated with eight physical properties such as the boiling point, critical temperature, critical pressure, critical volume, evaporation heat, density, heat capacity, surface tension, and three thermodynamic properties such as standard enthalpy, standard entropy and standard formation free energy of alkanes. A series of empiric equations for calculating the properties were obtained. Correlation coefficients of nine properties were more than 0.99. Regression analysis and calculation results indicated that the topological indices were well correlated with the physico-chemical properties of alkanes, and the novel topological index was far superior to eccentric connectivity index in the correlation.

A Novel Topological Index F and Its Correlation With Standard Formaton Enthalpies of AB_n(g) Molecules

The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F’* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, n=1 -4) and these correlation coefficients are all more than 0.96. Some molecules (e.g CH4, SiH4,etc. )can be preferably handled by F* but can not be dealt with by other topological indices. By contrast to traditional hydrogen suppressed graph, the contribution of hydrogen atoms to structures and properties of molecules is considered.

Prediction of the Physical Properties for the Ionic Liquid Based on Topological Index

Based on the distance matrix and adjacent matrix of molecular structure, a novel topological index is proposed. A set of topological parameters is built to reflect the magnitude, shape and other structure information of the substance. The interdependency between new topological index and conductivity for alkylimidazolium cations was analyzed and a quantitative relationship to describe this interdependency was obtained using the linear analyzing method. The analysis results show that the proposed topological index is quite satisfied with higher precision of the prediction. From the molecular structure of ionic liquid, the value of conductivity can be predicted correctly. This method can be also used to predict other physical properties of the ionic liquid.

A NEWLY-PROPOSED TOPOLOGICAL INDEX AND ITS APPLICATION

This paper proposed a topological index S which combined the graph feature and chemical surroundings. It can reflect the essential properties of chemical compounds better. The capacity of distinguishing structural isomers of saturated hydrocarbons is high.

Studies on the Physical Properties of Alkanes Using Edge-adjacency Information Topological Index

Edge-adjacency index and information topological index for 82 molecules of alkanes have been constructed and calculated. The topological indices were used to correlate with seven physical properties of the alkanes. Some empirical equations were obtained through regression. The regression and calculation results show a good agreement of the topological indices and the properties.

ELECTRONEGATIVITY TOPOLOGICAL INDEX AND ITS APPLICATION IN CORRELATION WITH MX,MX_2,MX_3,MX_4 MOLECULAR PROPERTIES

A New electronegativity topological index is defined and used to correlate with properties of MX,MX_2,MX_3,MX_4.

Topological Aspects of Dendrimers via Connection-Based Descriptors

Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.

Topological index associated with transverse axial vector and vector anomalies in QED

It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiyah- Singer index theorem.

Calculation of topological connectivity index for minerals

Topological method was applied firstly to calculate the topological connectivity index of minerals (TCIM). The reciprocal of effective atomic refractivity of metal element in minerals was chosen as its valence. The reasonability of TCIM as an activity criterion was tested through comparison of TCIM with two kinds of electronegativity parameter, i.e. ionic percentage and energy criteria of Yang’s electronegativity, solubility product, energy criterion according to the generalized perturbation theory and adsorption of flotation reagents on the surface of minerals. The results indicated that TCIM is an effective structural parameter of minerals to study the structure activity relationship. In addition, different mineral is of different TCIM value, so TCIM brings about convenience in comparison of flotation activity for minerals.

Computing Topological Invariants of Triangular Chandelier Lattice

A numerical parameter mathematically derived from the graph structure is a topological index.The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds.Here,we investigate some old degree-based topological indices like Randic index,sum connectivity index,ABC index,GA index,1st and 2nd Zagreb indices,modified second Zagreb index,redefined version of 1st,2nd and 3rd Zagreb indices,hyper and augmented Zagreb indices,forgotten index and symmetric division degree index,and some new degree-based indices like SK index,SK1 index,SK2 index,and AG1 index of triangular chandelier-lattice(TCL).The results are generalized by using edge partition and closed formulas for topological indices of triangular chandelier-lattice are analysed.

Novel Distance-Related Matrix Index and QSPR Research for Thermodynamics of Methyl Halides

A novel topological index W F is defined by the matrices X,W and L as W F=XWL.The topological index WF based on the distance-related matrix of molecular graphs is used to code the structural environment of each atom-type in a molecular graph.Good QSPR models have been obtained for standard formation enthalpy of methyl halides.The result indicates that the idea of using multiple matrices to define the distance-related matrix topological index is valid.

Schultz Polynomials and Their Topological Indices of Jahangir Graphs J2,m

Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J2,m for all integer number m ≥ 3 are calculated.

The First Eccentric Zagreb Index of Linear Polycene Parallelogram of Benzenoid

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as Σuv∈E(G)x(du+dv) and Σe=uv∈E(G)(du+dv) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg1*=Σuv∈E(G)(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.

Application Layer Multicast Model with Low Delay and High Stability

As an alternative of Internet protocol(IP)multicast,application layer multicast(ALM)is widely used with the advantage of simplicity and flexibility.However,the existing problems of large transmission delay and poor stability limit the application and development.In this article,to solve these problems,an ALM model based on node potential(NP)and topological index(TI)is proposed.The proposed model considers the factors of node capability and node distance in constructing and maintaining multicast tree to reduce transmission delay and increase stability,and thus it improves the application level in real-time multimedia multicast.The computer simulations prove that the proposed model reduces the ALM transmission delay,increases multicast tree stability effectively,and improves the ALM performance,and therefore it is suitable to apply in large-scale real-time multimedia environment.

Quantitative Structure-Property Relationship Research of Main Group Compounds

New appronches were applied to improve the molecular connectivity indices m^X^τ. The vertex valence is redefined and it was reasonable for hydrogen atom. The distances between vertices were used to propose novel connectivity topological indexes. The vertices and the distances in a molecular graph were taken into account in this definition. The linear regression was used to develop the structural property models. The results indicate that the novel connectivity topological indexes are useful model parameters for Quantitative Strncture-Property Relationship （ QSPR ） analysis.

Effects of thermodynamics parameters on mass transfer of volatile pollutants at air-water interface

A transient three-dimensional coupling model based on the compressible volume of fluid （VOF） method was developed to simulate the transport of volatile pollutants at the air-water interface. VOF is a numerical technique for locating and tracking the free surface of water flow. The relationships between Henry＇s constant, thermodynamics parameters, and the enlarged topological index were proposed for nonstandard conditions. A series of experiments and numerical simulations were performed to study the transport of benzene and carbinol. The simulation results agreed with the experimental results. Temperature had no effect on mass transfer of pollutants with low transfer free energy and high Henry＇s constant. The temporal and spatial distribution of pollutants with high transfer free energy and low Henry＇s constant was affected by temperature. The total enthalpy and total transfer free energy increased significantly with temperature, with significant fluctuations at low temperatures. The total enthalpy and total transfer free energy increased steadily without fluctuation at high temperatures.

The root structures of 21 aquatic plants in a macrophyte-dominated lake in China

Aims Aquatic plants play an important role in freshwater ecosystems.Previous works have largely focused on the functional significance of plant above ground parts,with much less attention on the root structures of aquatic plants.In this study,we divided 21 aquatic plants(including five introduced plants)into multiple plant groups(different life forms,monocot/eudicot and introduced/native)with the goal of addressing two questions:(i)what root structures do aquatic plants exhibit,and(ii)are there differences among these plant groups?Methods Twenty-one aquatic plants belonging to four life forms(free-float-ing,emergent,floating-leaved and submerged)were collected at the near flowering stage from a typical macrophyte-dominated lake in the yangtze River Basin,China.The following root topological parameters were quantified:altitude(a),path length(pe),magnitude(M),mean topological length(b),topological index(TI)and normed indices qa and qb.Important Findings The root topological indices TI,qa and qb for the 21 aquatic plants were 0.724±0.013,0.290±0.031 and 0.152±0.024(means±S.E.),respectively,revealing a general pattern of dichotomous branching,except for the aquatic root of Myriophyllum aquati-cum(Vell.)Verdc.,which displays herringbone branching.All three topological indices were significantly lower for monocots(TI=0.700±0.130,qa=0.191±0.149 and qb=0.086±0.236)than eudicots(TI=0.752±0.206,qa=0.405±0.569 and qb=0.229±0.393),indicating that the roots of monocots are typi-cally more dichotomous-like than those of eudicots.Among the four life forms,the three topological indices for emergent plants(TI=0.832±0.006,qa=0.616±0.018 and qb=0.381±0.014)were significantly higher than those of the other three life forms.Overall,there was no difference between the topological indices of introduced and native aquatic plants,but the introduced species M.aquaticum and Alternanthera philoxeroides(Mart.)Griseb.had both aquatic and edaphic roots as well as unusual functions,which may help explain their strong viability.