• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.757-774
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• 2022

Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), d_H(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ₂(G) = min_uv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ₂(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ₂(G) is sharp.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.43 no.9 s.351
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• pp.53-58
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• 2006

A Vertex Shader is designed to show more 3D graphics expressions, and to increase flexibility of the fixed function T&L (Transform and Lighting) engine. Design of this Shader is based on Vertex Shader 1.1 of DirectX 8.1 and OpenGL ARB. The Vertex Shader consists of four floating point ALUs for vectors operation. The previous 32bits floating point data type is replaced to 24bits floating point data type in order to design the Vertex Shader that consume low-power and occupy small area. A Xilinx Virtex2 300M gate module is used to verify behaviour of the core. The result of Synopsys synthesis shows that the proposed Vertex Shader performs 115MHz speed at the TSMC 0.13um process and it can operate as the rate of 12.5M Polygons/sec. It shows the complexity of 110,000 gates in the same process.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1990.04a
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• pp.312-325
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• 1990

This paper addresses the process of information dissemination in a network whereby a message, originated at a node, is transmitted to all other nodes of the network. We restrict our attention to a speccial type of dissemination process,called 'local broadcasting', where a vertex can either transmit or receive a message and an informed vertex can transmit it to only one of its neighbors at a time. Based on the recently published results for a tree by Koh and Tcha, this paper proposes an efficient heuristic which determines the call sequence at each vertex node under both minimax and minisum criteria. Computational experiments with this heuristic are conducted on a variety of networks of medium size.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.959-986
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• 2023

Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ${\rho}(G){\leq}{\sqrt{{\lfloor}{\frac{n^2}{4}}{\rfloor}}}$, and equality holds if and only if G is $K_{{\lceil}{\frac{n}{2}}{\rceil},{\lfloor}{\frac{n}{2}}{\rfloor}}$. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.16.1-16
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• 2003

A subset S of vertices of a graph G is independent if no two vertices of S are adjacent by an edge in G. Also we say that S is maximal independent if it is contained In no larger independent set in G. A planted plane tree is a tree that is embedded in the plane and rooted at an end-vertex. A (k＋1) -valent tree is a planted plane tree in which each vertex has degree one or (k＋1). We classify maximal independent sets of (k＋1) -valent trees into two groups, namely, type A and type B maximal independent sets and consider specific independent sets of these trees. We study relations among these three types of independent sets. Using the relations, we count the number of all maximal independent sets of (k＋1) -valent trees with n vertices of degree (k＋1).

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.6
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• pp.65-72
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• 2009

This paper presents a vision based localization method for indoor mobile robots using the types of vertices from a monocular image. In the images captured from a camera of a robot, the types of vertices are determined by searching vertical edges and their branch edges with a geometric constraints. For obtaining correspondence between the comers of a 2-D map and the vertex of images, the type of vertices and geometrical constraints induced from a geometric analysis. The vertices are matched with the comers by a heuristic method using the type and position of the vertices and the comers. With the matched pairs, nonlinear equations derived from the perspective and rigid transformations are produced. The pose of the robot is computed by solving the equations using a least-squares optimization technique. Experimental results show that the proposed localization method is effective and applicable to the localization of indoor environments.

• Proceedings of the KSRS Conference
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• v.1
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• pp.417-420
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• 2006

In these days, mobile application dealing with information contents on mobile or handheld devices such as mobile communicator, PDA or WAP device face the most important industrial needs. The motivation of this study is the design and implementation of mobile application using high resolution satellite imagery, large-sized image data set. Although major advantages of mobile devices are portability and mobility to users, limited system resources such as small-sized memory, slow CPU, low power and small screen size are the main obstacles to developers who should handle a large volume of geo-based 3D model. Related to this, the previous works have been concentrated on GIS-based location awareness services on mobile; however, the mobile 3D terrain model, which aims at this study, with the source data of DEM (Digital Elevation Model) and high resolution satellite imagery is not considered yet, in the other mobile systems. The main functions of 3D graphic processing or pixel pipeline in this prototype are implemented with OpenGL|ES (Embedded System) standard API (Application Programming Interface) released by Khronos group. In the developing stage, experiments to investigate optimal operation environment and good performance are carried out: TIN-based vertex generation with regular elevation data, image tiling, and image-vertex texturing, text processing of Unicode type and ASCII type.

• Journal of Korean Ophthalmic Optics Society
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• v.13 no.4
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• pp.9-12
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• 2008

Purpose: Current gas-mask is very uncomfortable structure for spectacles wearer. Improving this problem can aid military men and firemen to protect themselves and rescue other person. Methods: we changed the structure from dual type of outward lens and inward lens into a single type structure. we attached acrylic frame to gas-mask instead of outward lens and protected the gas inflow by shutting the gab of lens and frame using silicon shield, and made the frame "S" style for removing astigmatism and maintaining of vertex distance. Results: It was possible to correct visual acuity and gas shield, and could changed the lens like a common spectacles. The new type of gas-mask spectacles could remove 0.53D~1.78D astigmatism occurred from the slant of eyesight and lens surface, 0.07D~0.66D overcorrection occurred from short vertex distance, and 0.1D~0.3D astigmatism occurred from pantoscopic angle. Conclusion: Because new type of gas-mask spectacles had clear visual field, it was expected to improve fighting power and rescue ability.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).