• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.741-752
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• 2023

A new variant of vertex edge domination, namely semi total vertex edge domination has been introduced in the present paper. A subset S of the vertex set V of a graph G is said to be a semi total vertex edge dominating set(stved - set), if it is a vertex edge dominating set of G and each vertex in S is within a distance two of another vertex in S. An stved-set of G having minimum cardinality is said to be an γ_stve(G)- set and its cardinality is denoted by γ_stve(G). Bounds for γ_stve(G) - set have been given in terms of various graph theoretic parameters and graphs attaining the bounds have been characterized. In particular, bounds for trees have been obtained and extremal trees have been characterized.

• Proceedings of the Korean Information Science Society Conference
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• 2004.04a
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• pp.628-630
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• 2004

Distributed Denial of Service(D-DoS) 공격을 차단하기 위해서는 AS(Autonomous System) 경계 라우터에 필터를 설치하는 것이 필요하다. 필터가 설치되는 라우터의 개수를 최소로 하는 Vertex Cover(VC)--모든 edge를 커버하는 Vertex의 모임--을 찾아내는 방법은 NP-complete 문제가 된다. 따라서 Vertex Cover(VC) 근사기법 중에서 Greedy 알고리즘과 Approximated VC 알고리즘에 대해 Vertex Cover(VC)을 찾아내는 방법을 적용하여 실험하였다. Vertex Cover(VC)를 찾을 경우 Worst case에서 이론상 VC수의 최대 2배의 Vertex Cover(VC)를 찾아낼 수 있는 Approximated VC 알고리즘의 장점과 적은 수의 Vertex Cover(VC)로 모든 edge를 커버할 수 있는 Greedy 알고리즘［7］의 장점을 모두 갖춘 Vertex Cover(VC) 근사 기법을 구현하였다. NS-2를 이용한 실험 결과, 제안된 알고리즘은 Greedy 알고리즘보다 Vertex Cover를 찾아가는 단계 수에 따른 커버되는 층 노드 수를 비교하였을 때. 전체 노드의 75%를 커버하는데 24번의 단계가 필요하여 Greedy 알고리즘의 40개 보다 40%의 단계의 수적인 감소가 일어났으며 전체노드의 90%를 커버하는데 38%의 단계 개수의 감소가 일어났다. 실험으로 제안된 알고리즘이 Vertex Cover(VC) 톨 찾아가는 단계 측면에서 좀더 빠르게 AS 경계 라우터에 필터를 설치하여 D-DoS에 효율적으로 대처해 나갈 수 있음을 확인할 수 있다.

• Journal of Computing Science and Engineering
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• v.4 no.3
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• pp.207-224
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• 2010

This paper presents a compression scheme for mesh geometry, which is suitable for mobile graphics. The main focus is to enable real-time decoding of compressed vertex positions while providing reasonable compression ratios. Our scheme is based on local quantization of vertex positions with mesh partitioning. To prevent visual seams along the partitioning boundaries, we constrain the locally quantized cells of all mesh partitions to have the same size and aligned local axes. We propose a mesh partitioning algorithm to minimize the size of locally quantized cells, which relates to the distortion of a restored mesh. Vertex coordinates are stored in main memory and transmitted to graphics hardware for rendering in the quantized form, saving memory space and system bus bandwidth. Decoding operation is combined with model geometry transformation, and the only overhead to restore vertex positions is one matrix multiplication for each mesh partition. In our experiments, a 32-bit floating point vertex coordinate is quantized into an 8-bit integer, which is the smallest data size supported in a mobile graphics library. With this setting, the distortions of the restored meshes are comparable to 11-bit global quantization of vertex coordinates. We also apply the proposed approach to compression of vertex attributes, such as vertex normals and texture coordinates, and show that gains similar to vertex geometry can be obtained through local quantization with mesh partitioning.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.565-586
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• 2017

In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.361-369
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• 2018

For a given graph G = (V, E), a set $D{\subseteq}V(G)$ is said to be an outer-connected vertex edge dominating set if D is a vertex edge dominating set and the graph $G{\backslash}D$ is connected. The outer-connected vertex edge domination number of a graph G, denoted by ${\gamma}^{oc}_{ve}(G)$, is the cardinality of a minimum outer connected vertex edge dominating set of G. We characterize trees T of order n with l leaves, s support vertices, for which ${\gamma}^{oc}_{ve}(T)=(n-l+s+1)/3$ and also characterize trees with equal domination number and outer-connected vertex edge domination number.

• Journal of Broadcast Engineering
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• v.2 no.2
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• pp.94-104
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• 1997

This paper presents a new vertex-based binary shape coding scheme using one-dimensional vertex selection/encoding and vertex reordering. In compared with the conventional object-adaptive vertex encoding(OA VEL the extracted vertices are, firstly, classified into one-dimensional(lD) vertices and two-dimensional (2D) vertices in the proposed method. For lD vertices, new coding method proposed in this paper is performed. For 2D vertices, the vertex reordering and OA VE are carried out. Experimental results show that the proposed vertex-based coding scheme red.uces coding bits up to 12 % compared with the conventional one and its coding gain depends on the characteristics of contour.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.3
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• pp.121-127
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• 2004

This paper presents a new vertex selection scheme for shape approximation. In the proposed method, final vertex points are determined by "two-step procedure". In the first step, initial vertices are simply selected on the contour, which constitute a subset of the original contour, using conventional methods such as an iterated refinement method (IRM) or a progressive vertex selection (PVS) method In the second step, a vertex adjustment Process is incorporated to generate final vertices which are no more confined to the contour and optimal in the view of the given distortion measure. For the optimality of the final vertices, the dynamic programming (DP)-based solution for the adjustment of vertices is proposed. There are two main contributions of this work First, we show that DP can be successfully applied to vertex adjustment. Second, by using DP, the global optimality in the vertex selection can be achieved without iterative processes. Experimental results are presented to show the superiority of our method over the traditional methods.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.167-177
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• 2022

A vertex v of a graph G = (V, E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is called a double vertex-edge dominating set if every edge of E is ve-dominated by at least two vertices of S. The minimum cardinality of a double vertex-edge dominating set of G is the double vertex-edge domination number γ_dve(G). In this paper, we provide an upper bound on the double vertex-edge domination number of trees in terms of the order n, the number of leaves and support vertices, and we characterize the trees attaining the upper bound. Finally, we design a polynomial time algorithm for computing the value of γ_dve(T) for any trees. This gives an answer of an open problem posed in [4].

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.285-294
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• 2021

In the present work we introduce Gaussian vertex prime labeling and investigate Gaussian vertex prime labeling for gear graph, book graph, wheel graph, kayak paddle, one point union of gear graph and one point union of wheel graph.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.435-445
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• 2017

Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from $V(D){\cup}A(D){\rightarrow}\{1,2,{\ldots},p+q\}$ with the property that for every $v{\in}V(D)$, $f(v)+\sum_{u{\in}O(v)}f((v,u))=k$, for some constant k. Such a labeling is called a V-super vertex out-magic total labeling (V-SVOMT labeling) if $f(V(D))=\{1,2,3,{\ldots},p\}$. A digraph D is called a V-super vertex out-magic total digraph (V-SVOMT digraph) if D admits a V-SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V-SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies.