Modeling Gas Chromatographic Retention Indices of Oxygen-containing Compounds by Novel Atom-type Topological Indices

Quantitative structure-retention relationship （QSRR） model for the estimation of retention indices （RIs） of 39 oxygen-containing compounds containing ketones and esters was established by our newly introduced distance-based atom-type indices DAI. The useful application of the novel DAI indices has been demonstrated by developing accurate predictive equations for gas chromatographic retention indices. The statistical results of the multiple linear regression for the final model are τ=0.9973 and s=8.23. Furthermore, an external test set of 10 oxo-containing compounds can be accurately predicted with the final equation giving the following statistical results： τpred：0.9966 and spred=8.56.

On ev and ve-Degree Based Topological Indices of Silicon Carbides

In quantitative structure-property relationship(QSPR)and quantitative structure-activity relationship(QSAR)studies,computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures.Numerous topological indices have been inaugurated to describe different topological features.The ev and ve-degree are recently introduced novelties,having stronger prediction ability.In this article,we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si_(2)C_(3)−I[a,b].

On Some Ev-Degree and Ve-Degree Dependent Indices of Benes Network and Its Derived Classes

One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks,Benes networks,Interconnection networks,and David-derived networks using graph theoretic parameters.The topological indices(TIs)have been widely used as graph invariants among various graph theoretic tools.Quantitative structure activity relationships(QSAR)and quantitative structure property relationships(QSPR)need the use of TIs.Different structure-based parameters,such as the degree and distance of vertices in graphs,contribute to the determination of the values of TIs.Among other recently introduced novelties,the classes of ev-degree and ve-degree dependent TIs have been extensively explored for various graph families.The current research focuses on the development of formulae for different ev-degree and ve-degree dependent TIs for s−dimensional Benes network and certain networks derived from it.In the end,a comparison between the values of the TIs for these networks has been presented through graphical tools.

Some Topological Values of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine

L-valine is a glycogen-type amino acid regarded among the necessary mammalian amino acids.This is an amino acid that is essential for protein synthesis.N-salicylidene-L-valine is gaining a lot of attention because of its unique structure and increased catalytic and cytotoxic activity.We explore the chain of supramolecular dialkyltin N-salicylidene-L-valine complexes 2,3,and 4 to learn more about this structure and its features regarding topological indices.We computed the first and second Randi′c index,harmonic index,sum-connectivity index,atom-bond-connectivity index,geometric arithmetic index and reduced reciprocal Randi′c index of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine.Furthermore,we present an analysis of such structures using specific examples,as well as a comparison of topological indices.

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

The CellularNeuralNetwork(CNN)has various parallel processing applications,image processing,non-linear processing,geometric maps,highspeed computations.It is an analog paradigm,consists of an array of cells that are interconnected locally.Cells can be arranged in different configurations.Each cell has an input,a state,and an output.The cellular neural network allows cells to communicate with the neighbor cells only.It can be represented graphically;cells will represent by vertices and their interconnections will represent by edges.In chemical graph theory,topological descriptors are used to study graph structure and their biological activities.It is a single value that characterizes the whole graph.In this article,the vertex-edge topological descriptors have been calculated for cellular neural network.Results can be used for cellular neural network of any size.This will enhance the applications of cellular neural network in image processing,solving partial differential equations,analyzing 3D surfaces,sensory-motor organs,and modeling biological vision.

Comparative Study of Valency-Based Topological Descriptor for Hexagon Star Network

A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.

On Harmonic and Ev-Degree Molecular Topological Properties of DOX,RTOX and DSL Networks

Topological indices enable to gather information for the underlying topology of chemical structures and networks.Novel harmonic indices have been defined recently.All degree based topological indices are defined by using the classical degree concept.Recently two novel degree concept have been defined in graph theory:ve-degree and evdegree.Ve-degree Zagreb indices have been defined by using ve-degree concept.The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices.Dominating oxide,silicate and oxygen networks are important network models in view of chemistry,physics and information science.Physical and mathematical properties of dominating oxide,silicate and oxygen networks have been considerably studied in graph theory and network theory.Topological properties of the dominating oxide,silicate and oxygen networks have been intensively investigated for the last few years period.In this study we examined,the first,the fifth harmonic and ev-degree topological indices of dominating oxide(DOX),regular triangulene oxide network(RTOX)and dominating silicate network(DSL).

On Vertex-Edge-Degree Topological Descriptors for Certain Crystal Networks

Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences.The dynamical arrangement of vertices and their associated edges make them flexible(like liquid)to attain the shape of any physical structure or phenomenon easily.In the field of ICT they are used to reflect distributed component and communication among them.Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions.This area attracts the researchers due to its applications in theoretical and organic chemistry.It also inspires the mathematicians due to involvement of mathematical structures.Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences(vertex degrees).Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory.This paper reflects the work on topological indices such as ev-degree Zagreb index,the first ve-degree Zagrebindex,the first ve-degree Zagrebindex,the second ve-degree Zagreb index,ve-degree Randic index,the ev-degree Randic index,the ve-degree atom-bond connectivity index,the ve-degree geometric-arithmetic index,the ve-degree harmonic index and the ve-degree sum-connectivity index for crystal structural networks namely,bismuth tri-iodide and lead chloride.In this article we have determine the exact values of ve-degree and ev-degree based topological descriptors for crystal networks.

Vertex-Edge Degree Based Indices of Honey Comb Derived Network

Chemical graph theory is a branch of mathematics which combines graph theory and chemistry.Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks.It pulled the research community due to its applications in theoretical and organic chemistry since 1960.Additionally,it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.In this paper,we determined the newly introduced topological indices namely,first ve-degree Zagreb?index,first ve-degree Zagreb?index,second ve-degree Zagreb index,ve-degree Randic index,ve-degree atom-bond connectivity index,ve-degree geometric-arithmetic index,ve-degree harmonic index and ve-degree sum-connectivity index for honey comb derived network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure-activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.Also,we give the numerical and graphical representation of our outcomes.

Omega and Cluj-Ilmenau Indices of Hydrocarbon Molecules “Polycyclic Aromatic Hydrocarbons PAHk”

A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this paper, we computed the Omega and Cluj-Ilumenau indices of a very famous hydrocarbon named as Polycyclic Aromatic Hydrocarbons PAHk for all integer number k.

Simulation of ^(13)C NMR chemical shifts of carbinol carbon atoms using quantitative structure-spectrum relationships

A quantitative structure-spectrum relationship (QSSR) model was developed to simulate 13C nuclear magnetic resonance (NMR) spectra of carbinol carbon atoms for 55 alcohols. The proposed model,using multiple linear regression,contained four descriptors solely extracted from the molecular structure of compounds. The statistical results of the final model show that R2= 0.982 4 and S=0.869 8 (where R is the correlation coefficient and S is the standard deviation). To test its predictive ability,the model was further used to predict the 13C NMR spectra of the carbinol carbon atoms of other nine compounds which were not included in the developed model. The average relative errors are 0.94% and 1.70%,respectively,for the training set and the predictive set. The model is statistically significant and shows good stability for data variation as tested by the leave-one-out (LOO) cross-validation. The comparison with other approaches also reveals good performance of this method.

Ecological adaptation of Reaumuria soongorica root system architecture to arid environments

The architectural parameters of Reaumuria soongorica root system in different habitats of Gansu Province, China were analyzed to examine its ecological adaptability to arid environments. Results show that： （1） Topological indices of R. Soongorica root sys- tem are small in all habitats, and root branching pattem tends to be dichotomous. Also, the indices gradually increase in the Min- qin windblown sand region and the Zhangye Gobi region in Hexi Corridor, which indicates that drought tends to produce her- ringbone-like root branching pattems. （2） Fractal dimension values ofR. Soongorica root system are small and not obvious in the Minqin windblown sand region and the Zhangye Gobi region in Hexi Corridor, with values of 1.1778 and 1.1169, respectively. Fractal dimension values are relatively large in Jiuzhoutai semi-arid hilly and gully region of the Loess Plateau, which indicates that the R. Soongorica root system has better fractal characteristics in this region than in the other regions. （3） Total branching ra- tios of the R. Soongorica root system in arid regions of Hexi Corridor are smaller than that in the Jiuzhoutai semi-arid hilly and gully region of the Loess Plateau. This shows that root branching ability in the semi-arid region is stronger, and it decreases to some degree with increased drought. （4） The root connection lengths of R. soongorica root system are long in all habitats, but there are significant length differences between the different habitats. The root connection length at the Minqin windblown sand region is the longest. It is concluded that R. soongoriea adapts to arid environments by decreasing root branching, decreasing root overlap and increasing root connection length, which makes its root branching pattern tend to be herringbone-like to reduce com- petition in root internal environment for nutrients and to enhance root absorption rate of nutrients, and ensure effective nutrition space. Thus the roots can absorb enough water and nutrients in resource-poor settings to ensure normal physiological requirements.

Estimation of surface tension of organic compounds using quantitative structure-property relationship

A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.

Estimation of Stability Constants of Copper（Ⅱ） Complexes with a-Amino Acids Using Connectivity Index 3xV, Common Model for the Binary and Ternary Complexes

Models for estimation of the first （K1）, second （K2）, and overall stability constant （β2） of copper（II） chelates with naturally occurring amino acids, based on the valence connectivity index of the 3rd order （3Xr）, were improved by introduction of a square term and a new graph representation for mono-complexes （MLCor）. The models gave SE = 0.07, 0.05--0.07 and 0.05--0.08 for lg Ki, lg K2 and lg ,62 constants, respectively; models that encompass both bi- nary and ternary bis-complexes included indicator variable. We also validated our models on the test set which in- cluded two mono-, two binary and two ternary Cu（II） chelates with a-aminobutanoic acid and a-aminopentanoic acid, not included into the calibration. The absolute differences between experimental and predicted stability con- stants were in the range of 0.01--0.16.