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.

Quantitative Correlation between Group Connectivity Index and Property of Flotation Reagent

Topological method is applied firstly to calculate the group connectivity indexes of some flotation reagents for sulfide minerals and oxide minerals. The study reveals that some properties of flotation reagents, such as group electronegativity, energy criterion, solubility product of chemicals and maximum wavelength of ultraviolet absorbency, have linear correlation with the first order group connectivity index (GCI) of polar group, and the related coefficients are all larger than 0.900. The GCI can be used to characterize the structure of groups, and is a sort of new effective structural parameter to study the quantitative structure activity relationship of flotation reagents.

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.

On Eccentric Connectivity Index and Polynomial of Thorn Graph

The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized expressions for the eccentric connectivity index and polynomial of the thorn graphs, and then consider some particular cases.

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.

Study on Landscape Pattern Index-based Connectivity Analysis of the Primary Farmland Protection Zones

Farmland and primary farmland protection are important contents of land management and land use planning of China. In the new round of land use planning and database construction, primary farmland protection zones are required to have high integrity and connectivity. Using landscape pattern indexes, the integrity and connectivity of primary farmland protection zones was studied in Licheng District of Jinan City. The results showed that, except patch area standard deviation, the other indexes including average patch area, patch area variation coefficient, patch edge density, largest patch index, and mean euclidean nearest-neighbor, all indicate high connectivity of primary farmland protection zones after layout adjustment. A simple and convenient method for identifying the integrity and connectivity of primary farmland protection zones was supplied.

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.

ANALYSIS OF SOUTHEAST ASIAN NATIONS FIVE CONNECTIVITY INDEX

Located at the crossroads to Belt and Road connecting the continent and the sea, Southeast Asian countries are at the junction of some of the world’s most important sea routes. As the first countries to rally around the 21st Century Maritime Silk Road Initiative, Southeast Asian countries have been key partners and top priorities in construction of the Belt and Road promoted by China. After years of steady progress, China and Southeast Asian countries have secured great achievements in Belt and Road construction to enhance connectivity. According to a census conducted by a subject group, the overall performance of Southeast Asian countries ranked first compared to the other regions along the Belt and Road in 2017. Some countries in ASEAN region are seeing major improvements.

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

Optimal Deployment Patterns for k-Coverage and k-Connectivity 3D WSNs in Underground Tunnel

In this paper,we first model the mining structure as a arched shape in terms of the tunnel geometry.Based on the regularly placement of nodes in that model,a set of deployment patterns for seamless coverage and k-connectivity is proposed,i.e.1-and 2-connectivity.Further,we figure out the maximum horizontal distance of tangent plane to determine the placement of nodes for k-coverage（k=1,2）.Besides,the mathematical relations between the communication radius and the sensing radius are derived,when the network keeps k-coverage（k=1,2） and k-connectivity（k=2,3） under certain regularity constrains for various patterns.Finally,we demonstrate the optimality of several approaches that we have proposed in the aspect of energy consumption and network lifetime.

Abnormal Basal Ganglia Functional Connectivity in Idiopathic Generalized Epilepsy

The basal ganglia have been implicated in a modulation role in idiopathic generalized epilepsy （IGE） by an invasive electrophysioigic means. This paper investigates the basal ganglia functional connectivity by using the region-wise functional connection analysis in resting-state functional magnetic resonance imaging （fMRI） in IGE. The increased functional connectivity within basal ganglia, and between the basal ganglia and the thalamus, and decreased functional connectivity between basal ganglia and motor cortex are found in IGE compared with the controls. These findings not only implicate dysfunctional integration in the motor loop in IGE and the enhanced interaction in the modulated loop, but also suggest that the basal ganglia modulate the generalized epileptic discharges with the influence over thalamus in the corticothalamus network.

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 Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

图的Sum-connectivity指标与其无符号拉普拉斯谱半径

设G=(V,E)为简单连通图.图G的Sum-connectivity指标被定义为χ(G)=Σuv∈E(G)2/√d_(u)+d_(v),其中d_(u)表示顶点u的度.用q(G)表示图G的无符号拉普拉斯谱半径.本文研究了χ(G)与q(G)之间的关系,证明了对于所有顶点数n≥3的简单连通图G,都有q(G)/χ^(2)(G)≤n^(2)/(n-1)^(2)等式成立当且仅当G■S_(n).

关于Randic指数及图的直径

设图G=(V,E)是简单图,其中V是顶点集,E是边集.对G中任意顶点v∈V,dv表示点v的度数.图G的Ran-dic指数也称为图G的连通性指数,定义为R=R(G)=∑uv∈E 1dndv.关于连通图的Randic指数R与直径D有如下猜想:R-D≥2-n2+1且DR≥21+n2--11,两个等式都成立当且仅当G≌Pn.本文将简化该猜想,并进一步证明当D≤2(n-1)23n-3+2 2或D≤n-3时。

给定最大匹配数的树的零阶广义Randi指标

图G的零阶广义Randi指标定义为0Rα(G)=v∈V(G)d(v)α,其中d(v)为图G的顶点v的度,α为任意实数.研究了树的零阶广义Rα指标的极值问题,利用分析和图的理论,确定了任意给定最大匹配数的树的最大和最小Rα的值,并刻画了达到该极值的树.

直径不超过4的树的零阶广义Randi指数

图G=(V,E)为简单连通图,dv表示顶点v的度。G的零阶广义Randi指数定义为Rα0(G)=∑v∈Vdvα,其中α为任意实数。本文研究直径不超过4的树关于零阶广义Randi指数的极图问题。

转向细胞数为2的链状四角系统的Randi(c)指标

一个图(分子图)G的Randi(c)指标定义为图G的所有边uν上的权(d(u)d(ν))-12之和,其中(d(u)和d(ν))分别表示顶点u和ν的度.Randi(c)指标是化学图论中常见且重要的一个拓扑指标。本文给出了转向细胞数为2的链状四角系统的Randi(c)指标。

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.

两种分裂点连接运算图的Randic谱

对一个连通正则图G_(1)与任意一个正则图G_(2),基于分裂图SP(G_(1))与图G_(2)的两种运算,考虑对应新图类的Randic(规范化拉普拉斯,规范化无符号拉普拉斯)谱.利用这些结果,构造了关于上述三个矩阵的非正则的同谱图,并且计算了新构造图的度基尔霍夫指数和生成树的数目.