• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.47-55
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• 2005

For topological spaces X, Y and the function f : X → Y, it induces a function gr(f) : X → X x Y defined as gr(f)(χ) = (χ, f(χ)), for every χ ∈ X. It deals with some preliminary investigations relating to the behavior of functions and its graph functions. It has also been found that continuous functions are homotopic if and only if their graph functions are homotopic.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.227-245
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• 2014

Suppose G is a simple graph. The ${\ell}$-eigenvalues ${\delta}_1$, ${\delta}_2$,..., ${\delta}_n$ of G are the eigenvalues of its normalized Laplacian ${\ell}$. The normalized Laplacian Estrada index of the graph G is dened as ${\ell}EE$ = ${\ell}EE$(G) = ${\sum}^n_{i=1}e^{{\delta}_i}$. In this paper the basic properties of ${\ell}EE$ are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ${\ell}EE$ and graph energy $E_{\ell}$(G) are presented.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.467-475
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• 2020

Let G be a chemical graph with vertex set {v₁, v₁, …, v_n} and degree sequence d(G) = (deg_G(v₁), deg_G(v₂), …, deg_G(v_n)). The inverse degree, R(G) of G is defined as $R(G)={\sum{_{i=1}^{n}}}\;{\frac{1}{deg_G(v_i)}}$. The cyclomatic number of G is defined as γ = m - n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.875-877
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• 2003

그래프 분할문제에서 대량의 그래프 데이터를 처리하는 것은 계산에서 걸리는 시간보다 파일 입출력을 수행하는 데 걸리는 시간의 비중이 크다. 본 논문은 수행 속도와 분할 성능에 있어서 우수한 그래프 분할 알고리즘 중 하나인 Multilevel Graph Partitioning에 대해 입출력 효율을 높일 수 있도록 확장하는 기법을 제안하고 그 구현에 대해 기술한다. 그래프를 컴퓨터의 가용 메모리를 기준으로 서브 그래프로 나누어 메모리 참조의 지역성이 향상되도록 기존의 Multilevel Graph Partitioning을 확장 하였다. 기존의 방식과 제안된 방식을 테스트 그래프들에 적용하여 그 수행시간을 비교한 결과 그래프 데이터의 크기가 컴퓨터의 주 메모리의 용량에 비해 어느 수준 이상으로 커지면서 제안된 알고리즘이 기존의 방식보다 수행시간에 있어서 좋은 결과를 보인다.

• International Union of Geodesy and Geophysics Korean Journal of Geophysical Research
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• v.25 no.1
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• pp.23-34
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• 1997

Seismic tomography using the graph theoretical method of ray tracing is performed in two synthetic data sets with laterally varying velocity structures. The straight-ray tomography shows so poor results in imaging the laterally varying velocity structure that the ray-traced tomographic techniques should be used. Conventional ray tracing methods have serious drawbacks, i.e. problems of convergence and local minima, when they are applied to seismic tomography. The graph theretical method finds good approximated raypaths in rapidly varying media even in shadow zones, where shooting methods meet with convergence problems. The graph theoretical method ensures the globally minimal traveltime raypath while bending methods often cause local minima problems. Especially, the graph theoretical method is efficient in case that many sources and receivers exist, since it can find the traveltimes and corresponding raypaths to all receivers from a specific source at one time. Moreover, the algorithm of graph theoretical method is easily applicable to the ray tracing in anisotropic media, and even to the three dimensional case. Among the row-active inversion techniques, the conjugate gradient (CG) method is used because of fast convergence and high efficiency. The iterative sequence of the ray tracing by the graph theoretical method and the inversion by the CG method is an efficient and robust algorithm for seismic tomography in laterally varying velocity structures.

• Journal of Korean Elementary Science Education
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• v.31 no.3
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• pp.386-397
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• 2012

The purpose of this study was to find a way to improve the science textbook graph through analyzing teachers' interpretation process with eye movement tracking when they try to read the science textbook graph. Participants in this project were 10 elementary school teachers while bar graphs, line graphs, pie charts in 2007 revision science textbooks were used as materials. SMI (SensoMotoric Instruments)' iView X TM RED 120 Hz was used in order to collect eye movement data. Although subjects paid attention to the title of the graph at first, the consequence of the eye fixation was changed by the composition of the graph in case of the rest of areas. In particular, the flow of visual attention and fixation time were affected by the form and configuration of the graph. The diversity of graph construction caused confusion in interpreting graphs; the manner of presenting title, the difference of background colors, size of characters, the name of X-axis and Y-axis. Out results showed that the conformation of graphs as well as the presentation of each factor should be composed in accordance with the educational purpose for helping users to easier understanding.

• Journal of KIISE:Software and Applications
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• v.31 no.10
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• pp.1266-1275
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• 2004

Bioinformatics is concerned with the creation and development of advanced information and computational technologies for problems in biology. It is divided into genomics, proteomics and metabolimics. In metabolimics, an organism is represented by metabolic pathway, i.e., well-displayed graph, and so the graph drawing tool to draw pathway well is necessary to understand it comprehensively. In this paper, we design an improved drawing algorithm. It enhances the readability by making use of the bipartite graph. Also it is possible to draw large graph properly by considering the facts that metabolic pathway graph is scale-free network and is composed of circular components, hierarchic components and linear components.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.

• The Journal of the Korea Contents Association
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• v.18 no.1
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• pp.465-475
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• 2018

Recently, as the use of social media and IoT has increased, large graph streams has been generating and studies on real-time processing for them have been actively carrying out. In this paper we propose a incremental graph stream processing scheme that reuses previous result data when the graph changes continuously. We also propose a cost model to selectively perform incremental processing and static processing. The proposed cost model computes the predicted value of the detection cost and the processing cost of the recalculation area based on the actually processed history and performs the incremental processing when the incremental processing is more profit than the static processing. The proposed incremental processing increases the efficiency by processing only the part that changes when the graph update occurs. Also, by collecting only the previous result data of the changed part and performing the incremental processing, the disk I/O costs are reduced. It is shown through various performance evaluations that the proposed scheme outperforms the existing schemes.

• Journal of the Korea Society of Computer and Information
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• v.19 no.5
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• pp.19-25
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• 2014

In this paper, I seek the chromatic number, the maximum number of colors necessary when adjoining vertices in the plane separated apart at the distance of 1 shall receive distinct colors. The upper limit of the chromatic number has been widely accepted as $4{\leq}{\chi}(G){\leq}7$ to which Hadwiger-Nelson proposed ${\chi}(G){\leq}7$ and Soifer ${\chi}(G){\leq}9$ I firstly propose an algorithm that obtains the minimum necessary chromatic number and show that ${\chi}(G)=3$ is attainable by determining the chromatic number for Hadwiger-Nelson's hexagonal graph. The proposed algorithm obtains a chromatic number of ${\chi}(G)=4$ assuming a Hadwiger-Nelson's hexagonal graph of 12 adjoining vertices, and again ${\chi}(G)=4$ for Soifer's square graph of 8 adjoining vertices. assert. Based on the results as such that this algorithm suggests the maximum chromatic number of a planar graph is ${\chi}(G)=4$ using simple assigned rule of polynomial time complexity to color for a vertex with minimum degree.