• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.977-986
• /
• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Proceedings of the IEEK Conference
• /
• 2005.11a
• /
• pp.751-754
• /
• 2005

In this paper, we designed a vertex shader for mobile devices. Proposed Vertex shader is compatible with the OpenGL ARB & DirectX 8.0 Vertex Shader 1.1 and is organized of modified IEEE-754 24 bits float point SIMD architecture. All float point arithmetic unit process 1 cycle operation with 100Mhz frequency more. We made a vertex shader demo system with Xilinx-Virtex II and get synthesis result that confirm 11M gates size at TSMC 0.13um @ 115MHz.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.267-277
• /
• 2015

In this paper we investigate the properties of (a, d)-vertex antimagic total labeling of a digraph D = (V, A). In this labeling, we assign to the vertices and arcs the consecutive integers from 1 to |V|+|A| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its out arcs. These sums form an arithmetical progression with initial term a and common difference d. We show the existence and non-existence of (a, d)-vertex antimagic total labeling for several class of digraphs, and show how to construct labelings for generalized de Bruijn digraphs. We conclude this paper with an open problem suitable for further research.

• The KIPS Transactions:PartB
• /
• v.15B no.6
• /
• pp.609-612
• /
• 2008

Let G = (V, E) be a simple undirected graph. The Minimum Vertex Cover (MVC) problem is to find a minimum subset C of V such that for every edge, at least one of its endpoints should be included in C. Like many other graph theoretic problems this problem is also known to be NP-hard. In this paper, we propose a genetic algorithm called LeafGA for MVC problem and show the performance of the proposed algorithm by applying it to several published benchmark graphs.

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

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.6
• /
• pp.179-186
• /
• 2011

This paper suggests the minimum number of vertex guards algorithm. Given n rooms, the exact number of minimum vertex guards is proposed. However, only approximation algorithms are presented about the maximum number of vertex guards for polygon and orthogonal polygon without or with holes. Fisk suggests the maximum number of vertex guards for polygon with n vertices as follows. Firstly, you can triangulate with n-2 triangles. Secondly, 3-chromatic vertex coloring of every triangulation of a polygon. Thirdly, place guards at the vertices which have the minority color. This paper presents the minimum number of vertex guards using dominating set. Firstly, you can obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, you can obtain dominating set from visibility graph or visibility matrix. This algorithm applies various art galley problems. As a results, the proposed algorithm is simple and can be obtain the minimum number of vertex guards.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.7A
• /
• pp.1017-1027
• /
• 2000

In this paper, we propose a new coding method based on the distance between vertex segments for vertex positions in the vertex-based shape coding. The pixel lines are divided into the segments of a fixed length, and the segments that have vertex pixels are called vertex segments. We analyze the probability distribution of the relative distance between vertex segments and prove that it depends only on the ratio between the number of vertices and the number of segments. Considering the coding efficiency and implementation complexity, we choose a particular ratio to make a code table. For each input image, the segment size is chosen according tothe ratio, and the relative segment distances are entropy coded. It is shown that the proposed method is efficient for the images with many vertices.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.10
• /
• pp.5171-5189
• /
• 2016

With the popularity of cloud computing, many data owners outsource their graph data to the cloud for cost savings. The cloud server is not fully trusted and always wants to learn the owners' contents. To protect the information hiding, the graph data have to be encrypted before outsourcing to the cloud. The adjacent vertex search is a very common operation, many other operations can be built based on the adjacent vertex search. A boolean adjacent vertex search is an important basic operation, a query user can get the boolean search results. Due to the graph data being encrypted on the cloud server, a boolean adjacent vertex search is a quite difficult task. In this paper, we propose a solution to perform the boolean adjacent vertex search over encrypted graph data in cloud computing (BASG), which maintains the query tokens and search results privacy. We use the Gram-Schmidt algorithm and achieve the boolean expression search in our paper. We formally analyze the security of our scheme, and the query user can handily get the boolean search results by this scheme. The experiment results with a real graph data set demonstrate the efficiency of our scheme.

• Journal of applied mathematics & informatics
• /
• v.42 no.2
• /
• pp.367-377
• /
• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• Journal of Radiation Protection and Research
• /
• v.28 no.3
• /
• pp.225-231
• /
• 2003

Up-front irradiation technique as 3-dimensional conformation, or intensity modulation has kept large proportion of brain tumors from being complicated with acute radiation reactions in the normal tissue during or shortly after radiotherapy. For years, we've cannot help but counting on 2-D vertex beam technique to reduce acute reactions in the brain tumor patients because we're not equipped with 3-dimensional planning system. We analyzed its advantages and limitations in the clinical application. From 1998 to 2001, vertex or oblique vertex beams were applied to 35 patients with primary brain tumor and 25 among them were eligible for this analysis. Vertex(V) plans were optimized on the reconstructed coronal planes. As the control, we took the bilateral opposed techniques(BL) otherwise being applied. We compared the volumes included in 105% to 50% isodose lines of each plan. We also measured the radiation dose at various extracranial sites with TLD. With vertex techniques, we reduced the irradiated volumes of contralateral hemisphere and prevented middle ear effusion at contralateral side. But the low dose volume increased outside 100%; the ratio of V to BL in irradiated volume included in 100%, 80%, 50% was 0.55+/-0.10, 0.61+/-0.10, and 1.22+/-0.21, respectively. The hot area within 100% isodose line almost disappeared with vertex plan; the ratio of V to BL in irradiated volume included in 103%, 105%, 108% was 0.14+/-0.14, 0.05./-0.17, 0.00, respectively. The dose distribution within 100% isodose line became more homogeneous; the ratio of volume included in 103% and 105% to 100% was 0.62+/-0.14 and 0.26+/-0.16 in BL whereas was 0.16+/-0.16 and 0.02+/-0.04 in V. With the vertex techniques, extracranial dose increased up to $1{\sim}3%$ of maximum dose in the head and neck region except submandibular area where dose ranged 1 to 21%. From this data, vertex beam technique was quite effective in reduction of unnecessary irradiation to the contralateral hemispheres, integral dose, obtaining dose homogeneity in the clinical target. But it was associated with volume increment of low dose area in the brain and irradiation toward the head and neck region otherwise being not irradiated at all. Thus, this 2-D vertex technique can be a useful quasi-conformal method before getting 3-D apparatus.