• Bulletin of the Korean Chemical Society
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• v.25 no.2
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• pp.253-259
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• 2004

Some new topological indices based on the distance matrix and Randic connectivity (as graph invariants) are proposed. The calculation of these indices is simple and they have good discriminating ability toward alkanes. Incorporating the number of carbon atoms to one of the calculated indices gives a highly correlating topological index (Sh index) which found to correlate with selected physicochemical properties of wide range of alkanes, specially, their boiling points. Most of the investigated properties are well modeled (with $r^2$> 0.99) by the Sh index. Meanwhile, the resulting regressions were compared with the results based on the well-established Randic and newly reported Xu indices and, in most cases, better results were obtained by the Sh index. Moreover, multiple linear regression analysis of the alkane properties via calculated indices gives highly correlating models with low standard errors.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.959-977
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• 2022

The topological indices are numerical parameters which determined the biological, physical and chemical properties based on the structure of the chemical compounds. One of the recently topological indices is the uphill Zagreb indices. In this paper, the formulae of some uphill Zagreb indices for a few graph operations of some graphs have been derived. Furthermore, the precise formulae of those indices for the honeycomb network have been found along with their graphical profiles.

• Journal of Korean Society of Rural Planning
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• v.7 no.1 s.13
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• pp.37-48
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• 2001

The purpose of this study is to suggest the landscape potential index for visualizing landscape information in the conservation of hilly landscape in urban fringe. For the visual and quantitative approach to topological landscape assessment, numerical entity data of DEM(digital elevation model) were processed with CAD-based utilities that we developed and were mainly focused on analysis of visibility and visual sensitivity. Some results, with reference in assessing greenbelt area of Eodeung Mt. in Gwangju, proved to be considerable in the landscape assessment of suburban hilly landscapes. 1) Since the viewpoints and viewpoint fields were critical to landscape structure, randomized 194 points(spatially 500m interval) were applied to assessing the generalized visual sensitivity, we called. Because there were similar patterns of distribution comparing to those by 56 points and 18 Points given appropriately, it could be more efficient by a few viewpoints which located widely. 2) Regressional function was derived to represent the relationships between probabilities of visibility frequency and the topological factors(topological dominance, landform complexity and relational aspect) of target field. 3) Visibility scores of each viewpoint were be calculated by summing the visual sensitivity indices within a scene. The scores to the upper part including ridge line have been more representative to overall distributions of visual sensitivities. Also, with sum of deviations of sensitivity indices from each single point's specific index to the weighting values of view points could be estimated rotationally. 4) The deviational distributions of visual sensitivity classes in the topological unit of target field were proved to represent the visual vulnerability of the landform. 5) Landscape potential indices combined with the visual sensitivity and the DGN(degree of green naturality) were proposed as visualized landscape information distributed by topological unit.

• Communications of the Korean Mathematical Society
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• v.7 no.1
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• pp.25-32
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• 1992

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.159-167
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• 2024

The Topological indices are known as Mathematical characterization of molecules. In this paper, we have studied line graph of subdivision and semi-total point graph of triangular benzenoid, polynomino chains of 8-cycles and graphene sheet through forgotten and first Zagreb indices.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.205-225
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• 2022

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSO_α for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.663-680
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• 2024

The zero divisor graph is the most basic way of representing an algebraic structure as a graph. For any commutative ring R, each element is a vertex on the zero divisor graph and two vertices are defined as adjacent if and only if the product of those vertices equals zero. In this research, we determine some topological indices such as the Wiener index, the edge-Wiener index, the hyper-Wiener index, the Harary index, the first Zagreb index, the second Zagreb index, and the Gutman index of zero divisor graph of integers modulo prime power and its direct product.

• Bulletin of the Korean Chemical Society
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• v.35 no.5
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• pp.1413-1416
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• 2014

A novel topological index (TG Index) has been introduced. The graphical matrix representation of the TG index includes the use of directed subgraphs for the first time in graph theory literature. The application of the TG index on certain properties of polyenes yielded very well correlation data.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1589-1595
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• 2018

Similarity index measures the topological proximity of node pairs in a complex network. Numerous similarity indices have been defined and investigated, but the dependency of structure on the performance of similarity indices has not been sufficiently investigated. In this study, we investigated the relationship between the performance of similarity indices and structural properties of a network by employing a two-state random network. A node in a two-state network has binary types that are initially given, and a connection probability is determined from the state of the node pair. The performances of similarity indices are affected by the number of links and the ratio of intra-connections to inter-connections. Similarity indices have different characteristics depending on their type. Local indices perform well in small-size networks and do not depend on whether the structure is intra-dominant or inter-dominant. In contrast, global indices perform better in large-size networks, and some such indices do not perform well in an inter-dominant structure. We also found that link prediction performance and the performance of similarity are correlated in both model networks and empirical networks. This relationship implies that link prediction performance can be used as an approximation for the performance of the similarity index when information about node type is unavailable. This relationship may help to find the appropriate index for given networks.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.365-377
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• 2015

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n₁ $\leq$ n₂, n₁ + n₂ = n and p < n₁ be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph K_n1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.