• Kyungpook Mathematical Journal
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• 제56권4호
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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 ${\Gamma}_S(N)$.

• 한국통신학회논문지
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• 제40권12호
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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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• 제22권9호
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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.

• 호남수학학술지
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• 제27권4호
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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.

• 한국콘텐츠학회논문지
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• 제8권5호
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• pp.52-60
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• 2008

위성 통신 분야에서 널리 사용되는 시분할 다중 스위칭 시스템은 많은 저대역폭 가입자들로부터 발생되는 트랙픽을 반복되는 프레임에 타임 슬롯을 할당해야 한다. 본 논문에서는 타임 슬롯 할당을 위한 새로운 방법을 제안한다. 기존의 방법인 네트워크 흐름 모델을 사용하지 않고 새로운 방법인 그래프 채색방법을 사용하여 효율적인 타임 슬롯 할당 알고리즘을 제안하였다. 제안된 알고리즘은 주어진 트래픽의 프레임 길이가 2의 멱승일 경우 트래픽을 정확히 반으로 나누어 할당한다. 분할된 트래픽의 프레임 길이가 1이 될 때까지 이 과정을 계속적으로 반복해 분할한다. 제안된 알고리즘의 시간 복잡도는 프레임의 길이가 L이고 스위치 크기가 N인 경우에는 기존의 네트워크 흐름 모델을 사용한 최적의 타임 슬롯 할당 알고리즘의 시간 복잡도는 $O(N^{4.5})$ 인데 반해 $O(NLlog_2L)$이다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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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.

• 전자공학회논문지
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• 제53권6호
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• pp.80-87
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• 2016

본 논문에서는 그래프 컬러링과 OpenMP를 사용한 병렬 메쉬 스무딩 알고리즘을 제안하고 공유메모리 기반의 슈퍼컴퓨터를 이용하여 제안하는 병렬 메쉬 스무딩 알고리즘의 성능 분석을 수행하였다. 제안하는 병렬 메쉬 스무딩 알고리즘은 그래프 컬러링 방법을 통해 전체 메쉬를 여러 개의 독립적인 집합 (색깔)으로 나눈 후 각각의 독립적인 집합에 대하여 OpenMP 라이브러리를 사용하여 순차적으로 병렬 메쉬 스무딩을 수행하는 방법이다. 실험을 통하여 여러 가지 그래프 컬러링 방법과 색깔 순서 재배열 방법이 병렬 메쉬 스무딩의 효율성에 미치는 영향에 대해서 알아보았다. 또한, OpenMP의 루프 스케줄링 방법이 병렬 메쉬 스무딩의 효율성에 끼치는 영향에 대해서 알아보았다.

• 대한산업공학회지
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• 제25권2호
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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.

• 대한수학회보
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• 제50권4호
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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].

• 대한산업공학회지
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• 제18권2호
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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.