• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.171-186
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• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.1003-1006
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• 2005

Vertex shader of GPU in personal computer is advanced in functions as to be half of traditional fixed T&L functions. And, capacity of memory for saving resources to process instructions is unlimited. GPU that can be programmed by programmer is needed for mobile system as well as personal computer. In this paper, we implement software virtual machine for vertex shader using C++ Language. Our goal is designing hardware GPU that can apply to mobile system. The virtual machine consists of nVidia GPU instructions. Input Data to virtual machine is generated by Microsoft fxc compiler. That is to say, Input Data is compiled shader program written in HLSL, Cg, or ASM. The virtual machine will be a reference model for designing hardware GPU and can be used for Testbed to test added or modified instruction.

• Journal of computational fluids engineering
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• v.9 no.1
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• pp.48-56
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• 2004

The numerical simulations with unstructured mesh by cell-centered and vertex-centered approaches were peformed for the quadrilateral and triangular meshes. For 2-D inviscid supersonic vortex flow, the simulation results and the analytic solution were compared and the accuracy was assessed. The calculation efficiency was measured by the parameter defined by the consumed CPU time multiplied by absolute error As a results, equilateral triangular mesh yielded the best accuracy and efficiency among the tested meshes. Cell-centered approach gives a little better efficiency than vertex - centered approach.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.12
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• pp.1548-1555
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• 1999

본 논문에서는 하이퍼그래프의 {{{{k분 분할을 위한 서열화(vertex ordering) 알고리즘의 효율을 개선하기 위한 후처리 알고리즘인 재서열법을 소개한다. 제안된 알고리즘은 {{{{k분 분할을 위한 다양한 알고리즘에 쉽게 적용될 수 있다. 보통 초기 분할은 서열화를 기반으로 하는 알고리즘에 의해 형성된다. 그 후 제안된 알고리즘은 클러스터와 정점을 재배열하여 분할하는 과정을 반복함으로써 분할의 효율을 향상시켜간다. 이 방법을 여러 가지 그래프에 적용하여 향상된 결과를 얻었다.Abstract This paper addresses the post-processing algorithm for {{{{k-way hypergraph partitioning by using a cluster and vertex reordering method. The proposed algorithm applies to several {{{{k-way partitioning algorithm. Generally, the initial partition generating method is based on a vertex ordering algorithm. Our reordering algorithm construct an enhanced partitioning by iteratively partition the reodered clusters and vertices. Experimental results on several graphs demonstrate that reodering provides substantial enhancement.

• Journal of electromagnetic engineering and science
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• v.13 no.1
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• pp.16-21
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• 2013

This study presents the angular effects of virtual vertices inserted for effective treatment of the boundary edge laid on an infinite conducting surface in a half-space scattering problem. We investigated the angular effects of virtual vertices by first computing the radar cross section (RCS) of a specific scatterer; i.e., a tilted conducting plate in contact with the ground surface, by inserting the virtual vertex in half-space. Here, the electric field integral equation is used to solve this problem with various virtual vertex angles (${\theta}_{\nu}$) and conducting plate inclination angles (${\theta}_r$) ranging from $0^{\circ}$ to $180^{\circ}$. The effects of the angles ${\theta}_{\nu}$ and ${\theta}_r$ on the RCS computation are clearly shown with numerical results with and without the virtual vertices in free- and half-spaces.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.759-773
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• 2009

A dominating set for a graph G is a set D of vertices of G such that every vertex of G not in D is adjacent to a vertex of D. Reed [11] considered the domination problem for graphs with minimum degree at least three. He showed that any graph G of minimum degree at least three contains a dominating set D of size at most $\frac{3}{8}$ |V (G)| by introducing a covering by vertex disjoint paths. In this paper, by using this technique, we show that every graph on n vertices of minimum degree at least four contains a dominating set D of size at most $\frac{4}{11}$ |V (G)|.

• Journal of the Korean Society of Safety
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• v.22 no.5
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• pp.41-49
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• 2007

In general, the curved structures have the engineering efficiency as well as a fine view compared with straight member. Also, composite materials are composed of two or more different materials to produce desirable properties for structural strength as compared to single ones. Shell structures with composite materials have many advantages in strength and weight reduction. Therefore, composite laminated conical shells are analyzed in this study. To solve differential equations of conical shells, this paper used finite difference method. Various parametric study according to the change of radius ratio, vertex angle and subtended angle are examined. The change of radius ratio, vertex angle and subtended angle mean the change from conical shells to cylindrical shells, conical shells to circular plates and open shells closed shells, respectively.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.44-53
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• 2007

A three-dimensional viscous flow solver has been developed for the prediction of the aerodynamic performance of hovering helicopter rotor blades using unstructured hybrid meshes. The flow solver utilized a vertex-centered finite-volume scheme that is based on the Roe's flux-difference splitting with an implicit Jacobi/Gauss-Seidel time integration. The eddy viscosity are estimated by the Spalart- Allmaras one-equation turbulence model. Calculations were performed at three operating conditions with varying tip Mach number and collective pitch setting for the Caradonna-Tung rotor in hover. Additional computations are made for the UH-60A rotor in hover. Reasonable agreements were obtained between the present results and the experiment in both blade loading and overall rotor performance. It was demonstrated that the present vertex-centered flow solver is an efficient and accurate tool for the assessment of rotor performance in hover.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.445-451
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• 1993

For the calculation of transonic laminar flow fields in cascades of turbomachinery, a finite volume method employing Jameson's Runge-Kutta integration scheme as a basic algorithm is presented. The cell-vertex scheme introducing half-spacing mesh cells is developed. For the velocity gradients in the stress terms the integration with divergence theorem is used for the average concept. Some numerical results show good agreement with experimental data.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.307-315
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• 2018

Let G be a simple connected graph with n vertices and m edges, with a sequence of vertex degrees $d_1{\geq}d_2{\geq}{\cdots}{\geq}d_n$ > 0. A vertex-degree topological index, referred to as harmonic index, is defined as $H={\sum{_{i{\sim}j}}{\frac{2}{d_i+d_j}}$, where i ~ j denotes the adjacency of vertices i and j. Lower and upper bounds of the index H are obtained.