Search Results (20)

In recent years, the accelerated pace of urbanization has increased patch fragmentation, which has had a certain impact on the structure and ecological environment of forest–grass ecological networks, and certain protection measures have been taken in various regions. Therefore, studying the spatiotemporal changes and correlations of ecological service functions and forest–grass ecological networks can help to better grasp the changes in landscape ecological structure and function. This paper takes the Wuding River Basin as the research area and uses the windbreak and sand fixation service capacity index, soil conservation capacity, and net primary productivity (NPP) to evaluate the ecological service capacity of the research area from the three dimensions of windbreak and sand fixation, soil conservation, and carbon sequestration. The Regional Sustainability and Environment Index (RSEI) is used to extract ecological source areas, and GIS spatial analysis and the minimum cumulative resistance (MCR) model are used to extract potential ecological corridors. Referring to complex network theory, topology metrics such as degree distribution and clustering coefficient are calculated, and their correlation with ecological service capacity is explored. The results show that the overall ecological service capacity of sand fixation, soil fixation, and carbon sequestration in the research area in 2020 has increased compared to 2000, and the ecological flow at the northern and northwest boundaries of the river basin has been enhanced, but there are still shortcomings such as fragmented ecological nodes, a low degree of clustering, and poor connectivity. In terms of the correlation between topology indicators and ecological service functions, the windbreak and sand fixation service capacity index have the strongest correlation with clustering and the largest grasp, while the correlation between soil conservation capacity and eigencentrality is the strongest and has the largest grasp. The correlation between NPP and other indicators is not obvious, and its correlation with eccentricity and eigencentrality is relatively large. Full article

A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let $\mathcal{R}$ be a commutative ring with identity, and $Z^{*}(\mathcal{R})$ is the set of all non-zero zero divisors of $\mathcal{R}$. Then, $\Gamma (\mathcal{R})$ is said to be a zero-divisor graph if and only if $a·b=0$, where $a,b\in V(\Gamma (\mathcal{R}))=Z^{*}(\mathcal{R})$ and $(a,b)\in E(\Gamma (\mathcal{R}))$. We define $a\sim b$ if $a·b=0$ or $a=b$. Then, ∼ is always reflexive and symmetric, but ∼ is usually not transitive. Then, $\Gamma (\mathcal{R})$ is a symmetric structure measured by the ∼ in commutative rings. Here, we will draw the zero-divisor graph from commutative rings and discuss topological indices for a zero-divisor graph by vertex eccentricity. In this paper, we will compute the total eccentricity index, eccentric connectivity index, connective eccentric index, eccentricity based on the first and second Zagreb indices, Ediz eccentric connectivity index, and augmented eccentric connectivity index for the zero-divisor graph associated with commutative rings. These will help us understand the characteristics of various symmetric physical structures of finite commutative rings. Full article

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network. Full article

The general eccentric connectivity index of a graph R is defined as ${\xi }^{ec}\left(R\right)={\sum }_{u\in V\left(G\right)}d\left(u\right)ec{\left(u\right)}^{\alpha }$, where $\alpha$ is any real number, $ec\left(u\right)$ and $d\left(u\right)$ represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds. Full article

The connective eccentricity index (CEI) of a hypergraph $\mathcal{G}$ is defined as ${\xi }^{ce}\left(\mathcal{G}\right)={\sum }_{v\in V\left(\mathcal{G}\right)}\frac{d_{\mathcal{G}}\left(v\right)}{{\epsilon }_{\mathcal{G}}\left(v\right)}$, where ${\epsilon }_{\mathcal{G}}\left(v\right)$ and $d_{\mathcal{G}}\left(v\right)$ denote the eccentricity and the degree of the vertex v, respectively. In this paper, we determine the maximal and minimal values of the connective eccentricity index among all k-uniform hypertrees on n vertices and characterize the corresponding extremal hypertrees. Finally, we establish some relationships between the connective eccentricity index and the eccentric connectivity index of hypergraphs. Full article

A two-mode network is a type of network in which nodes can be divided into two sets in such a way that links can be established between different types of nodes. The relationship between two separate sets of entities can be modeled as a bipartite network. In computer networks data is transmitted in form of packets between source to destination. Such packet-switched networks rely on routing protocols to select the best path. Configurations of these protocols depends on the network acquirements; that is why one routing protocol might be efficient for one network and may be inefficient for a other. Because some protocols deal with hop-count (number of nodes in the path) while others deal with distance vector. This paper investigates the minimum transmission in two-mode networks. Based on some parameters, we obtained the minimum transmission between the class of all connected n-nodes in bipartite networks. These parameters are helpful to modify or change the path of a given network. Furthermore, by using least squares fit, we discussed some numerical results of the regression model of the boiling point in benzenoid hydrocarbons. The results show that the correlation of the boiling point in benzenoid hydrocarbons of the first Zagreb eccentricity index gives better result as compare to the correlation of second Zagreb eccentricity index. In case of a connected network, the first Zagreb eccentricity index ${\xi }_1(\aleph )$ is defined as the sum of the square of eccentricities of the nodes, and the second Zagreb eccentricity index ${\xi }_2(\aleph )$ is defined as the sum of the product of eccentricities of the adjacent nodes. This article deals with the minimum transmission with respect to ${\xi }_i(\aleph )$, for $i=1,2$ among all n-node extremal bipartite networks with given matching number, diameter, node connectivity and link connectivity. Full article

A graph G is called an ℓ-apex tree if there exist a vertex subset $A\subset V\left(G\right)$ with cardinality ℓ such that $G-A$ is a tree and there is no other subset of smaller cardinality with this property. In the paper, we investigate extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index, and consequently for the Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others. For the one extreme value we obtain that the extremal graph is a join of a tree and a clique. Regarding the other extreme value, which turns out to be a harder problem, we obtain results for $\ell =1$ and pose some open questions for higher ℓ. Symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including topological indices of graphs. Full article

A fullerene is a cubic three-connected graph whose faces are entirely composed of pentagons and hexagons. Entropy applied to graphs is one of the significant approaches to measuring the complexity of relational structures. Recently, the research on complex networks has received great attention, because many complex systems can be modelled as networks consisting of components as well as relations among these components. Information—theoretic measures have been used to analyze chemical structures possessing bond types and hetero-atoms. In the present article, we reviewed various entropy-based measures on fullerene graphs. In particular, we surveyed results on the topological information content of a graph, namely the orbit-entropy I_a(G), the symmetry index, a degree-based entropy measure I_λ(G), the eccentric-entropy If_σ(G) and the Hosoya entropy H(G). Full article

This article is devoted to the determination of edge-based eccentric topological indices of a zero divisor graph of some algebraic structures. In particular, we computed the first Zagreb eccentricity index, third Zagreb eccentricity index, geometric-arithmetic eccentricity index, atom-bond connectivity eccentricity index and a fourth type of eccentric harmonic index for zero divisor graphs associated with a class of finite commutative rings. Full article

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed. Full article

Extreme rainstorms have important socioeconomic consequences, but understanding their fine spatial structures and temporal evolution still remains challenging. In order to achieve this, in view of an evolutionary property of rainstorms, this paper designs a process-oriented algorithm for identifying and tracking rainstorms, named PoAIR. PoAIR uses time-series of raster datasets and consists of three steps. The first step combines an accumulated rainfall time-series and spatial connectivity to identify rainstorm objects at each time snapshot. Secondly, PoAIR adopts the geometrical features of eccentricity, rectangularity, roundness, and shape index, as well as the thematic feature of the mean rainstorm intensity, to match the same rainstorm objects in successive snapshots, and then tracks the same rainstorm objects during a rainstorm evolution sequence. In the third step, an evolutionary property of a rainstorm sequence is used to extrapolate its spatial location and geometrical features at the next time snapshot and reconstructs a rainstorm process by linking rainstorm sequences with an area-overlapping threshold. Experiments on simulated datasets demonstrate that PoAIR performs better than the Thunderstorm Identification, Tracking, Analysis and Nowcasting algorithm (TITAN) in both rainfall tracking and identifying the splitting, merging, and merging-splitting of rainstorm objects. Additionally, applications of PoAIR to Integrated Multi-satellitE Retrievals for Global Precipitation Mission (GPM/IMERG) final products covering mainland China show that PoAIR can effectively track rainstorm objects. Full article

Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs. Full article

Chemical graph theory comprehends the basic properties of an atomic graph. The sub-atomic diagrams are the graphs that are comprised of particles called vertices and the covalent bond between them are called edges. The eccentricity ${ϵ}_u$ of vertex u in an associated graph G, is the separation among u and a vertex farthermost from u. In this article, we consider the precious stone structure of cubic carbon and registered Eccentric-connectivity index $\xi \left(G\right)$ , Eccentric connectivity polynomial $ECP(G,x)$ and Connective Eccentric index $C^{\xi }\left(G\right)$ of gem structure of cubic carbon for n-levels. Full article

Graph theory is successfully applied in developing a relationship between chemical structure and biological activity. The relationship of two graph invariants, the eccentric connectivity index and the eccentric Zagreb index are investigated with regard to anti-inflammatory activity, for a dataset consisting of 76 pyrazole carboxylic acid hydrazide analogs. The eccentricity ${\epsilon }_v$ of vertex v in a graph G is the distance between v and the vertex furthermost from v in a graph G. The distance between two vertices is the length of a shortest path between those vertices in a graph G. In this paper, we consider the Octagonal Grid $O_n^m$ . We compute Connective Eccentric index $C^{\xi }\left(G\right)={\sum }_{v\in V\left(G\right)}{d}_v/{\epsilon }_v$ , Eccentric Connective Index $\xi \left(G\right)={\sum }_{v\in V\left(G\right)}{d}_v{\epsilon }_v$ and eccentric Zagreb index of Octagonal Grid $O_n^m$ , where $d_v$ represents the degree of the vertex v in G. Full article

In this article, we study the chemical graph of a cyclic octahedron structure of dimension n and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index, the second Zagreb index, the third Zagreb index, the atom bond connectivity index and the geometric arithmetic index of the cyclic octahedron structure. Furthermore, we give the analytically closed formulas of these indices which are helpful for studying the underlying topologies. Full article