The atom-bond connectivity index of chemical bicyclic graphs

The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.

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.

Morphodynamics and sediment connectivity index in an unmanaged,debris-flow prone catchment:a through time perspective

Torrential processes are among the main actors responsible for sediment production and mobility in mountain catchments.For this reason,the understanding of preferential pathways for sediment routing has become a priority in hazard assessment and mitigation.In this context,the sediment Connectivity Index(IC)enables to analyse the existing linkage between sediment sources and the selected target(channel network or catchment outlet).The IC is a grid-based index that allows fast computation of sediment connectivity based on landscape information derived from a single Digital Terrain Model(DTM).The index computation is based on the log-ratio between an upslope and a downslope component,including information about drainage area,slope,terrain roughness,and distance to the analysis target(e.g.outlet).The output is a map that highlights the degree of structural connectivity of sediment pathways over analysed catchments.Until now,these maps are however rarely used to help defining debris-flow hazard maps,notably due to a lack of guidelines to interpret the IC spatial distribution.This paper proposes an exploitation procedure along profiles to extract more information from the analysis of mapped IC values.The methodology relies on the analysis of the IC and its component variables along the main channel profile,integrated with information about sediment budgeting derived from Difference of DEMs(DoD).The study of connectivity was applied in the unmanaged sub-catchment(without torrent control works)of the Rio Soial(Autonomous Province of Trento–NE Italy)to understanding the geomorphic evolution of the area after five debris flows(in ten years)and the related changes of sediment connectivity.Using a recent DTM as validation,we demonstrated how an IC analysis over the older DTM can help predicting geomorphic changes and associated hazards.The results show an IC aptitude to capture geomorphic trajectories,anticipate debris flow deposits in a specific channel location,and depict preferential routing pathways.

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.

Spatial connectivity and distribution of landscape type in the natural secondary forests of eastern mountainous region,northeast China——a case study of Mao'ershan region in Heilongjiang Province

Mao'ershan region is representative in the natural secondary forested region of the eastern mountainous region, northeast China. The landscape nearest neighbor index and landscape connectivity index were calculated with ARC/INFO software for Mao'ershan region. The spatial distribution of the landscape of the region was analyzed. The results showed that the landscape connectivity index of non-woodland was significantly higher than that of woodland. The landscape connectivity index of natural forest was nearly equal to zero, which means its fragmentation degree is high. The nearest neighbor index of plantation was lower than that of natural forest and non-forestland. Among the man-made forests, the distance index of the coniferous mixed plantation is the lowest, and its pattern is nearly glomeration. The landscape pattern of natural forest presented nearly random distribution. Among non-forest land, the distance index of cut blank was the lowest, and its pattern was also nearly glomeration. Keywords Landscape type - Landscape pattern - Nearest neighbor index - Landscape connectivity index - Natural secondary forest - Northeast China CLC number S759.92 Document code A Foundation item: This paper was supported by the Key Project of State Department of Science Technology (2002BA515B040).Biography: LI SHu-juan (1977), female. Lecture in Ocean University of China, Qingdao 266003, P. R. China.Responsible editor: Zhu Hong

Condensed Extended Hyper-Wiener Index

According to the definitions of molecular connectivity and hyper-Wiener index, a novel set of hyper-Wiener indexes （Dn, ^mDn） were defined and named as condensed extended hyper-Wiener index, the potential usefulness of which in QSAR/QSPR is evaluated by its correlation with a number of C3-C8 alkanes as well as by a favorable comparison with models based on molecular connectivity index and overall Wiener index.

On the maximal eccentric connectivity indices of graphs

For a connected simple graph G, the eccentricity ec（v） of a vertex v in G is the distance from v to a vertex farthest from v, and d（v） denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξC（G）, is defined as ∑vЕV（G） d（v）ec（v）. In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges（n ≤ m ≤ n ＋ 4）, and propose a conjecture on the graphs with maximal eccentric connectivity index and m edges （m ≥ n ＋ 5）. among the connected graphs with n vertices

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.

Computation of Topological Indices of Dutch Windmill Graph

In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic connectivity index of Dutch windmill graph.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

A New Model for Prediction of Surface Tension of Pure Fluids

A new model based on the theoretical work of Boudh-Hir and Mansoori was developed for prediction of surface tension of pure fluids. The new model has the advantage of not requiring densities in the calculation, and the input parameters are critical temperature and connectivity indices. A total of 209 compounds covering a wide variety of substances were used to develop the model, and the overall correlative AAD is 4.21%. To test its predictive ability, the model is further used to predict the surface tension of 25 more compounds that were not included in the model development. The overall predictive AAD is 4.07%, which illustrates that the model is reliable. The model proposed is simple and easy to apply, with good predictive accuracy.

Prediction of aqueous solubility of PCBs based on molecular structure

The thermodynamic relationships among aqueous solubility and molar volume (MV) , total molecular surface area (TSA) and molecular connectivity index (MCI) for highly hydrophobic chemicals. PCBs are established and discussed, respectively. Good linear relationships exist among In Cs and MV, TSA or MCI.

QSPR Analysis of the Physicochemical Properties for Phthalic Acid Esters

Based on quantitative structure-property relationship （QSPR） of organic compounds, the molecular connectivity indices of 21 phthalic acid ester compounds were extracted. Relationship between the physicochemical properties （n-octanol/air partition coefficient, vapor pressure, water solubility） and the molecular connectivity indices of phthalic acid ester compounds have been established by multiple linear regression （MLR） method. The results showed that the zero-order valence connectivity index （0Xu） is the topology parameter which affects octanol/water partition coefficient and water solubility, and the topology parameter which affects vapor pressure is the first-order connectivity index （1X）. This indicated to a certain extent_that the molecular connectivity indices can be well used to express the quantitative relationship between the physicochemical properties and structure descriptions of phthalic acid ester compounds. The models constructed have good robustness and highly predictive capability.

On the ECI and CEI of (3, 6)-Fullerenes

The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentricity have a wide range of applications in structure-activity relationships and pharmaceutical drug design etc. In this paper, we investigate the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene. We find a relation between the radius and the number of spokes of a (3, 6)-fullerene. Based on the relation, we give the computing formulas of the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene, respectively.

Prediction of Antagonistic Activity of <i>β</i>-Carboline and Its Derivatives Using Topological Descriptors

Prediction of antagonistic activity of β-carboline and its thirteen derivatives has been made using topological descriptors viz, connectivity index, and kappa shape index of different orders. For evaluation of values of descriptor, molecular modeling and geometry optimization of all the compounds were carried out with CAChe Pro software by opting semiempirical PM3 method using MOPAC 2002. For prediction of activity multiple linear regression analysis (MLR) was performed. MLR analysis has been made by Project Leader Software associated with CAChe by using the above descriptors as independent variables and biological activity as dependent variables. We were performed leave-one-out methods and the result reflected a direct relationship between biological activity and connectivity index of zero order, while indirect relationship with connectivity index of second order and thus connectivity index is a reliable descriptor to predict the biological activity of β-carboline and its various derivatives.

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.

Research on Tourism Agglomeration: A Case Study of Hainan Province, China

On the basis of analyzing yearly data and spatial relationships between tourism spots, star hotels and travel agencies of Hainan Province, and comparing all the methods of measuring industrial spatial agglomeration, this paper chose Hefindahl index, Location Quotient, nearest neighbor index, spatial connection index and geographic concentration index to measure Hainan tourism agglomeration. By applying these methods, total tourism agglomeration, agglomeration of tourism factors and regional agglomeration differences were studied. The results showed that the overall agglomeration increases as time flows, and the eastern part is the most agglomerated, the west takes the second, with the middle ranking the least. The large-scale agglomeration regions are Sanya and Haikou. The influencing factors of Hainan tourism spatial agglomeration were concluded as tourism resource endowment, industrial attributes, geographic conditions, governmental policies and the overall economic development level, etc. In addition, the paper proposed tourism spatial agglomeration modes of Hainan Province at various spatial scales.

On the Eigenvalues of General Sum-Connectivity Laplacian Matrix

The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and has been applied to studying network structures.In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index.We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix,as well as its spectral diameter.We show the corresponding extremal graphs.In addition,we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.

Quantitative Structure Property Relations （QSPR） for Predicting Molar Diamagnetic Susceptibilities, xm, of Inorganic Compounds

For predicting the molar diamagnetic susceptibilities of inorganic compounds, a novel connectivity index ^mG based on adjacency matrix of molecular graphs and ionic parameter gi was proposed. The gi is defined as gi=（ni^0.5-0.91）^4·xi^0.5｜Zi^0.5, where Zi, ni, xi are the valence, the outer electronic shell primary quantum number, and the electronegativity of atom i respectively. The good QSPR models for the molar diamagnetic susceptibilities can be constructed from ^0G and ^1G by using multivariate linear regression （MLR） method and artificial neural network （NN） method. The correlation coefficient r, standard error, and average absolute deviation of the MLR model and NN model are 0.9868, 5.47 cgs, 4.33 cgs, 0.9885, 5.09 cgs and 4.06 cgs, respectively, for the 144 inorganic compounds. The cross-validation by using the leave-one-out method demonstrates that the MLR model is highly reliable from the point of view of statistics. The average absolute deviations of predicted values of the molar diamagnetic susceptibility of other 62 inorganic compounds （test set） are 4.72 cgs and 4.06 cgs for the MLR model and NN model. The results show that the current method is more effective than literature methods for estimating the molar diamagnetic susceptibility of an inorganic compound. Both MLR and NN methods can provide acceptable models for the prediction of the molar diamagnetic susceptibilities. The NN model for the molar diamagnetic susceptibilities appears more reliable than the MLR model.

Lattice Energy Estimation for Complex Inorganic Ionic Crystal

A novel connectivity index ^mG based on adjacency matrix of molecular graphs was proposed as follows： ^mG = ∑（gi·gj·g…）^0.5. The element gi of adjacency matrix was defined as gi=（1＋Zi^1.4）/（1＋ri^1.4）, where Zi and ri are the charge number and the thermochemical radius of ion i respectively, and the radii ri for metal ions are taken to be the Goldschmidt radius. The regression analysis by the connectivity index 1G can provide a high-quality QSPR model for the lattice energies of 245 complex inorganic ionic crystal samples. The results imply, that the lattice energies may be expressed as a linear model of the connectivity index 1G. For the linear model the correlation coefficient r and the standard error s are 0.9998 and 228.72 kJ/mol, respectively. The cross-validation by the leave-one-out method demonstrates that the model is highly reliable from the point of view of statistics.