• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.863-874
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• 1999

세분화란 초기 원형 모델의 삼각형 메쉬를 여러 개의 작은 메쉬로 변환하는 기법으로, 간략화 된 모델을 다시 원상태로 표현하기 위해 사용된다. 기존의 보간에 의한 세분화는 전체 모델의 에지에 일률적으로 세분화를 적용하기 때문에, 효과가 적은 부분까지도 세분화가 수행하게 되어 효율이 떨어진다. 본 논문에서는 정점 변화율을 기반으로 에지를 선택하여 세분화를 수행한다. 따라서 원형 메쉬를 변환하여 세분화된 메쉬를 생성할 때, 모델의 각 부분들은 정점 변화율의 차이에 의해 서로 다른 세분화 정도를 가지게 된다. 이 과정을 통해 원형 모델의 곡률 특성이 반영된 세분화를 수행할 수 있게 되고, 전체 모델의 세분화 정도를 조정하는 것도 가능해진다. Abstract The subdivision is a mesh transformation, which makes an original triangle mesh to subdivided meshes. This method is used for recovering original model from simplified model. The existing subdivision based on interpolation is inefficient, because it is targeted for whole edges of mesh model. Therefore, this method applies to non-effective parts. In this paper the subdivision is executed by edge selection based on curvature. When original model is transformed to subdivided model by proposed method, the parts of model has different subdivision degrees by means of the averages of vertex curvature.Proposed method makes it enable subdivision, which deploy characteristics of curvatures of original model and adjusting a degree of subdivision in whole model.

• 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.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.325-327
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• 2007

We report a simple area measurement device for 3 dimensional object using 3 degree of freedom sensor. The surface of 3D object can be divided into a number of triangles, and the surface area of 3D object could be measured by the sum of the divided triangle area. We applied 6DOF sensor to measure the coordinate of triangle vertex, and calculated each triangle area on the surface of 3D object. The many we divide the area to triangles, the correct we will get the result. This method shows 7.78% in error on the measurement of 3 dimensional object area.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.2
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• pp.60-65
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• 2008

The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any $m{\geq}4$, the matching preclusion numbers of both m-dimensional restricted HL-graph and recursive circulant $G(2^m,4)$ are equal to degree m of the networks, and that every minimum matching preclusion set is the set of edges incident to a single vertex.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.40-51
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• 2009

A paired many-to-many k-disjoint path cover (paired k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants G($cd^m$,d) with $d{\geq}3$ and tori, and show that provided the number of faulty elements (vertices and/or edges) is f or less, every nonbipartite recursive circulant and torus of degree $\delta$ has a paired k-DPC for any f and $k{\geq}1$ with $f+2k{\leq}{\delta}-1$.

• Journal of the Speleological Society of Korea
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• no.88
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• pp.38-44
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• 2008

This study aims to identify the efficiency by applying diverse index to the positions of vertex in the network among the network analysis methods in order to identify the relational location features of caves. The first consideration was about the relational location features according to the linking degree and centrality of cave. The second consideration was about the structural equivalence between caves or between caves and the surrounding tourists attractions. A variety of index examined in this study is very efficient for identifying the positions of caves in the network. Furthermore, the relational location features in consideration of surrounding tourists attractions identified the availability of more objective and quantitative expression. In particular, when there are other caves around a cave, it is also very useful to identify the structural equivalence or comparison with other caves.

• 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.