• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1103-1113
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• 2016

In this paper, we study a directed simple graph ${\Gamma}_S(N)$ for a near-ring N, where the set $V^*(N)$ of vertices is the set of all left N-subsets of N with nonzero left annihilators and for any two distinct vertices $I,J{\in}V^*(N)$, I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph ${\Gamma}_S(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph ${\Gamma}_S(N)$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.12
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• pp.2410-2418
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• 2015

In this paper, we consider the femto users and their mutual interference as graph elements, nodes and weighted edges, respectively. The total bandwidth is divided into a number of resource blocks (RBs) and these are assigned to the femto user equipment (FUEs) using a graph coloring algorithm. In addition, resources blocks are assigned to the femto users to avoid inter-cell interference. The proposed scheme is compared with the traditional scheduling schemes in terms of throughput and fairness and performance improvement is achieved by exploiting the graph coloring scheme.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.31-34
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• 2022

The concept of locating chromatic number of graph is a development of the concept of vertex coloring and partition dimension of graph. The locating-chromatic number of G, denoted by χ_L(G) is the smallest number such that G has a locating k-coloring. In this paper we will discussed about the procedure for determine the locating chromatic number of Origami graph using Python Programming.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.551-559
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• 2005

A permutation graph over a graph G is a generalization of both a graph bundle and a graph covering over G. In this paper, we characterize the F-permutation graphs over a graph whose chromatic numbers are 2. We determine the chromatic numbers of $C_n$-permutation graphs over a tree and the $K_m$-permutation graphs over a cycle.

• The Journal of the Korea Contents Association
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• v.8 no.5
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• pp.52-60
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• 2008

A simple Time Division Multiplex(TDM) switching system which has been widely in satellite networks provides any size of bandwidth for a number of low bandwidth subscribers by allocating proper number of time slots in a frame. In this paper, we propose a new approach based on graph coloring model for efficient time slot assignment algorithm in contrast to network flow model in previous works. When the frame length of an initial matrix of time slot requests is 2's power, this matrix is divided into two matrices of time slot requests using binary divide and conquer method based on the graph coloring model. This process is continued until resulting matrices of time slot requests are of length one. While the most efficient algorithm proposed in the literature has time complexity of $O(N^{4.5})$, the time complexity of the proposed algorithm is $O(NLlog_2L)$, where N is the number of input/output links and L is the number of time slot alloted to each link in the frame.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1695-1700
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• 2005

In this paper, we propose an optimal thresholding method for the voxel coloring in the reconstruction of a 3D shape. Our purposed method is a new approach to resolve the trade-off error of the threshold value on determining the photo-consistency in the conventional method. Optimal thresholding value is decided to compare the surface voxel of photo-consistency with inside voxel on the optic ray of the center camera. As iterating the process of the voxels, the threshold value is approached to the optimal value for the individual surface voxel. And also, graph cut method is reduced to the surface noise on eliminating neighboring voxel. To verify the proposed algorithm, we simulated in the virtual and real environment. It is advantaged to speed up and accuracy of a 3D face reconstruction by applying the methods of optimal threshold and graph cut as compare with conventional algorithms.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.6
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• pp.80-87
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• 2016

We propose a parallel mesh smoothing algorithm using graph coloring and OpenMP library for shared memory many core computer architectures. The proposed algorithm partitions a mesh into independent sets and performs a parallel mesh smoothing using OpenMP library. We study the effect of using various graph coloring and color reordering algorithms on the efficiency of performing the proposed parallel mesh smoothing algorithm. We also investigate the influence of using various OpenMP loop scheduling methods on the parallel mesh smoothing efficiency.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.2
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• pp.226-232
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• 1999

Graph Coloring Problem(GCP) is a problem of assigning different colors to nodes which are connected by an edge. An extended form of GCP is TCP (T-coloring problem) and, in TCP, edge weights are added to GCP and it is possible to extend GCP's applications. To solve TCP, in this paper, we propose an improved Simulated Annealing(SA) method with search space smoothing. It has been observed that the improved SA method obtains better results than SA does.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1303-1314
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• 2013

An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors. A graph G is said to be injectively $k$-choosable if any list $L(v)$ of size at least $k$ for every vertex $v$ allows an injective coloring ${\phi}(v)$ such that ${\phi}(v){\in}L(v)$ for every $v{\in}V(G)$. The least $k$ for which G is injectively $k$-choosable is the injective choosability number of G, denoted by ${\chi}^l_i(G)$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G)={\Delta}(G)$. Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < $\frac{8k-3}{3k}$, then ${\chi}^l_i(G)={\Delta}(G)$ where $k={\Delta}(G)$ and ${\Delta}(G){\geq}6$. In addition, when ${\Delta}(G)=5$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{17}{7}$, and when ${\Delta}(G)=4$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{7}{3}$. These results generalize some of previous results in [1, 4].

• Journal of Korean Institute of Industrial Engineers
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• v.18 no.2
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• pp.43-49
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• 1992

Edge coloring problem is to find a minimum cardinality coloring of the edges of a graph so that any pair of edges incident to a common node do not have the same colors. Edge coloring problem is NP-hard, hence it is unlikely that there exists a polynomial time algorithm. We formulate the problem as a covering of the edges by matchings and find valid inequalities for the convex hull of feasible solutions. We show that adding the valid inequalities to the linear programming relaxation is enough to determine the minimum coloring number(chromatic index). We also propose a method to use the valid inequalities as cutting planes and do the branch and bound search implicitly. An example is given to show how the method works.