• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2021-2026
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• 2013

Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.541-551
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• 1998

Recently, the importance of participating in classes activity and cultivating student's thinking ability is emphasized in the mathematics education society. Teachers are demanded to change their teaching style centered pencile-and paper into using the variety instructional aids, such as calculator, video tape, computer, ohp, and projector, etc. In this paper, we search for the mathematica's function and the method that apply mathematical to the secondary school mathematics. Mathematical has many functions: calculator, algebra, graphics, animations, programing, notebook. We find that mathematica can be applied to the graph of function, the understand of simultaneous equations, the graph of trigonometry function, the calculation of limit, the computation of areas as limits, the derivative of a function and tangent line, a solid figure, and others in secondary school mathematics.

• Journal of Biomedical Engineering Research
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• v.38 no.2
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• pp.82-88
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• 2017

Enlargement of the lateral ventricles have been identified as a surrogate marker of neurological disorders. Quantitative measure of the lateral ventricle from MRI would enable earlier and more accurate clinical diagnosis in monitoring disease progression. Even though it requires an automated or semi-automated segmentation method for objective quantification, it is difficult to define lateral ventricles due to insufficient contrast and brightness of structural imaging. In this study, we proposed a fully automated lateral ventricle segmentation method based on a graph cuts algorithm combined with atlas-based segmentation and connected component labeling. Initially, initial seeds for graph cuts were defined by atlas-based segmentation (ATS). They were adjusted by partial volume images in order to provide accurate a priori information on graph cuts. A graph cuts algorithm is to finds a global minimum of energy with minimum cut/maximum flow algorithm function on graph. In addition, connected component labeling used to remove false ventricle regions. The proposed method was validated with the well-known tools using the dice similarity index, recall and precision values. The proposed method was significantly higher dice similarity index ($0.860{\pm}0.036$, p < 0.001) and recall ($0.833{\pm}0.037$, p < 0.001) compared with other tools. Therefore, the proposed method yielded a robust and reliable segmentation result.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

• Korean Journal of Microbiology
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• v.39 no.2
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• pp.67-75
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• 2003

One large topic in comparative genomics is to predict functional annotation by classifying protein sequences. Computational approaches for function prediction include protein structure prediction, sequence alignment and domain prediction or binding site prediction. This paper is on another computational approach searching for sets of homologous sequences from sequence similarity graph. Methods based on similarity graph do not need previous knowledges about sequences, but largely depend on the researcher's subjective threshold settings. In this paper, we propose a genome sequence clustering method of iterative testing and graph decomposition, and a simple method to calculate a strict threshold having biochemical meaning. Proposed method was applied to known bacterial genome sequences and the result was shown with the BAG algorithm's. Result clusters are lacking some completeness, but the confidence level is very high and the method does not need user-defined thresholds.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1351-1362
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• 2007

We enumerate the number of weighted complete graphs and compute its generating function.

• The Journal of Korean Association of Computer Education
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• v.17 no.6
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• pp.103-113
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• 2014

This study designed and implemented a query model for consecutive analyses of dynamic multivariate graph data. First, the query model consists of two procedures; setting the discriminant function, and determining an alteration method. Second, the query model was implemented as a query system that consists of a query panel, a graph visualization panel, and a property panel. A Node-Link Diagram and the Force-Directed Graph Drawing algorithm were used for the visualization of the graph. The results of the queries are visually presented through the graph visualization panel. Finally, this study used the data of worldwide import & export data of small arms to verify our model. The significance of this research is in the fact that, through the model which is able to conduct consecutive analyses on dynamic graph data, it helps overcome the limitations of previous models which can only perform discrete analysis on dynamic data. This research is expected to contribute to future studies such as online decision making and complex network analysis, that use dynamic graph models.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1463-1466
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• 1987

The problem of generating minimal area CMOS functional cell layout can be converted to that of decomposing the transistor connection graph into a minimum number of subgraphs, each having a pair of Euler paths with the same sequence of input labels on the N-graph and P-graph, which are portions of the graph corresponding to NMOS and PMOS parts respectively. This paper proposes a heuristic algorithm which yields a nearly minimal number of Euler paths from the path representation formula which represents the give a logic function. Subpath merging is done through a list processing scheme where the pair of paths which results in the lowest cost is successively merged from all candidate merge pairs until no further path merging and further reduction of number of subgraphs are possible. Two examples were shown where we were able to further reduce the number of interlaces, i.e., the number of non-butting diffusion islands, from 3 to 2, and from 2 to 1, compared to the earlier work [1].

• Proceedings of the KIEE Conference
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• 2004.05a
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• pp.65-67
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• 2004

Change of state of Channel between two wireless terminals which is caused by noise and multiple environmental conditions for happens frequently from the Wireles Network. So, When it is like that planning a wireless network protocol or performance analysis, it follows to change of state of time-varying channel and packet the analysis against a transmission efficiency is necessary. In this paper, analyzes transmission time of a packet and a packet in a time-varying and packet based Wireless Network. To reflecte the feature of the time-varying channel, we use a Signal Flow Graph model. From the model the mean of transmission time and the mean of queue length of the packet are analyzed in terms of the packet distribution function, the packet transmission service time, and the PER of the time-varying channel.