• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.339-358
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• 2021

Zagreb indices and their modified versions of a molecular graph are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. In this work, we investigate some properties of the modified second multiplicative Zagreb index of graphs with given connectivity. In particular, we obtain the maximum values of the modified second multiplicative Zagreb index with fixed number of cut edges, or cut vertices, or edge connectivity, or vertex connectivity of graphs. Furthermore, we characterize the corresponding extremal graphs.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Journal of the Korean Chemical Society
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• v.31 no.2
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• pp.143-152
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• 1987

$\pi$-Binding energy of the 153 kinds of unsaturated acyclic polyenes and unsaturated cyclic polyenes has been calculated by the Kier's Molecular Connectivity Index. An excellent linear correlation is found between HMO $\pi$-binding energy and $\pi$-binding energy calculated by the Kier's Molecular Connectivity Index. In either class of unsaturated acyclic hydrocarbons and unsaturated cyclic hydrocarbon, the regression analysis reveals a highly significant linear correlation between $E_{\pi}$ and $^1{\chi}^v$ (the first order valence connectivity index).

• Journal of Environmental Impact Assessment
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• v.21 no.3
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• pp.391-407
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• 2012

The loss of connectivity and fragmentation of forest landscapes are seriously hindering dispersal of many forest-dwelling species, which may be critical for their viability and conservation by decreasing habitat area and increasing distance among habitats. For understanding their environmental impacts, numerous spatial models exist to measure landscape connectivity. However, general relationships between functional connectivity and landscape structure are lacking, there is a need to develop landscape metrics that more accurately measure landscape connectivity in whole landscape and individual patches. We reviewed functional and structural definition of landscape connectivity, explained their mathematical connotations, and applied representative 13 indices in 3 districts of Seoul having fragmented forest patches with tits, the threshold distance was applied 500m by considering the dispersal of tits. Results of correlation and principal component analysis showed that connectivity indices could be divided by measurement methods whether they contain the area attribute with distance or not. Betweenness centrality(BC), a representative index measuring distance and distribution among patches, appreciated highly stepping stone forest patches, and difference of probability of connectivity(dPC), an index measuring including area information, estimated integrated connectivity of patches. Therefore, for evaluating landscape connectivity, it is need to consider not only general information of a region and species' characteristics but also various measuring methods of landscape connectivity.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.228-230
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• 2003

In this study, uses of remote sensed imagery in urban environment analysis are represented with the actual processed results with newly implemented programs running under ESRI ArcView-GIS to extract secondary information about mainly urban transportation environment. Implemented programs are about Accessibility index and Connectivity index. Accessibility index and Connectivity index are composed of four types of different algorithms and three types of algorithms such as alpha, gamma, and shimmel index. As show applied examples, tried to find out how remotely sensed imageries can be effectively utilized at actual processing in the direct or indirect ways in these algorithms.

• Journal of the Korean Chemical Society
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• v.31 no.2
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• pp.153-161
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• 1987

The carcinogenicity of benzenoid hydrocarbons apparently depends strongly on the topological nature of the molecule. The existance of certain regions in the structure which are known propensity of benzenoid hydrocarbons to be carcinogenic. We try to identify the correlation between the number of potentially carcinogenic bay region in each of them and the quantity of Molecular Connectivity Index for 81 benzenoid hydrocarbons. Results indicate an excellent linear correlation between the number of bay region and the quantity of molecular connectivity index except the molecular containing single bond in their structure.

• Journal of Korean Society of Transportation
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• v.28 no.6
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• pp.167-177
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• 2010

This study proposes a methodology for assessing the improvement of network connectivity of transport hubs. Extending a previously developed model that measures the connectivity of a node in transportation networks, we define two quantities called the supplied connectivity and the experienced connectivity. Using these quantities, we provide a systematic procedure for analyzing the network connectivity of a transport hub and also suggest criteria for determining whether a given project is effective in improving the network connectivity of the transport hub. The application of the methodology to a test site produces reasonable results, and as such it is expected that the methodology can be used for various transport hubs in the national road network. Once enough data from the application of the methodology are accumulated, a further study on the level of service in terms of network connectivity needs to be followed.

• Journal of Korean Society of Transportation
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• v.28 no.4
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• pp.129-139
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• 2010

This study proposes a model for measuring the connectivity of nodes in road networks. The connectivity index between two nodes is characterized by the number of routes, degree of circuitousness, design speed, and route capacity between the nodes. The connectivity index of a node is then defined as the weighted average of the connectivity indexes between the node and other nodes under consideration. The weighting factor between two nodes is determined by the travel demand and distance between them. The application of the model to a toy network shows that it reasonably well quantifies the level of connectivity of nodes in the network. If flow of rail networks can be measured in the same scale as that of road networks and the capacity of rail links can be estimated, the model proposed in this paper could be applied to intermodal transportation networks as well.

• Journal of Korean Society of Transportation
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• v.27 no.4
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• pp.195-206
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• 2009

The deregulation of aviation markets in Europe and the United Sates had led airlines to reconfigure their networks into hub-and-spoke systems. Recent trends of "Open Skies" in the Asian aviation market are also expected to prompt the reformation of airlines' networks in the region. A significant connectivity index is a crucial tool for airlines and airport authorities to estimate the degree of hub-and-spoke operations. Therefore, this paper suggests a new index, Continuous Indirect Connectivity Index (CICI), for measuring the coordination of airlines' flight schedules, applying it to the Asian, European and the American aviation markets. CICI consists of three components：(i) temporal connectivity to identify the attractiveness between connection flights, (ii) spatial connectivity to differentiate the attractiveness by de-routing distance with continuous linear function, and (iii) relative intensity to reflect the effect of direct flight frequency on transfer routes. CICI is evaluated to examine a casual relationship through regression analyses with two dependent variables of the number of transfer passengers and transfer rates. Compared with Danesi's index and Doganis' index through evaluation processes, CICI has a higher coefficient value of determination, implying that it explains the relationship between connectivity and transfer passengers more precisely.

• Korean Journal of Environment and Ecology
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• v.29 no.2
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• pp.263-278
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• 2015

This study is intended to evaluate the value of functional aspect from the viewpoint of habitat. The indicators that are used in biotope evaluations are various, but most of them use the criteria to evaluate the naturality. This evaluation method cannot appropriately reflect the functional characteristics coming from relation to the surrounding biotope. In this study, the connectivity, cohesion and diversity between individual biotope are quantitatively measured by a landscape index. It is hard to draw the functional value of individual biotopes because the landscape index related to connectivity, cohesion and diversity comes from a landscape having a number of biotopes. The concept of contribution was used to overcome this limitation. The concept of contribution is to quantify how much each individual biotope contributes to the connectivity, cohesion, and diversity in a certain range of landscape by deriving the amount of change in the landscape index according to the presence or absence of each individual biotope. In order to understand the characteristics of evaluation results in functional aspect, this research has done a comparative analysis of the previous research findings in the same target area. According to the result of the research, individual biotopes such as artificial forests, fragmented natural forests, and small planting sites were highly rated.