• 대한수학회보
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• 제59권1호
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• pp.119-139
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• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• International Journal of Computer Science & Network Security
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• 제23권7호
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• pp.61-70
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• 2023

Image segmentation is a very crucial step in effective digital image processing. In the past decade, several research contributions were given related to this field. However, a general segmentation algorithm suitable for various applications is still challenging. Among several image segmentation approaches, graph-based approach has gained popularity due to its basic ability which reflects global image properties. This paper proposes a methodology to partition the image with its pixel, region and texture along with its intensity. To make segmentation faster in large images, it is processed in parallel among several CPUs. A way to achieve this is to split images into tiles that are independently processed. However, regions overlapping the tile border are split or lost when the minimum size requirements of the segmentation algorithm are not met. Here the contributions are made to segment the image on the basis of its pixel using min-cut/max-flow algorithm along with edge-based segmentation of the image. To segment on the basis of the region using a homogenous optimum cut algorithm with boundary segmentation. On the basis of texture, the object type using spectral partitioning technique is identified which also minimizes the graph cut value.

• 전기의세계
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• 제22권5호
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• pp.12-18
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• 1973

This paper deals with Linear Programming by Signal Flow Graph technique which is different from that of Mason and Coates. The objective function is regarded as variable, and slack variable node, artificial variable node and objective function variable (constant) node are newly defined, which shows the process for optimization of solution very intuitively. Also methods for solving L.P. and examples with subject to Ax.leq.b, Ax=b and Ax.geq.b are presented.

• 대한수학회지
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• 제44권3호
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• pp.661-671
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• 2007

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.

• 전자공학회논문지A
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• 제31A권6호
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• pp.209-221
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• 1994

Timers are commonly used in hardware design for time delays that are to be much longer than the system clock period. In this paper, we present a method by which we can synthesie a hardware containing timers that implement long time delays described in VHDL. Because, in general, timers require high hardware cost, they must be utilized as efficiently as possible. To solve this problem we define a graph model and propose an algorithm that uses the graph model to minimize number of timers. A preliminary experimental result show that the algorithm implements all required time delays using minimum number of timers.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.641-644
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• 2000

This paper studies coverability tree and reach-ability set of Petri net under the earliest filing rule. Conventional algorithm for coverability tree for ‘normal’ Petri net is not good for Petri net under the earliest firing rule. More over, it is shown that there exists no coverability graph for general class of earliest firing Petri net. Some subclasses are studied where coverability graph can be constructed.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

• Industrial Engineering and Management Systems
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• 제7권2호
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• pp.84-92
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• 2008

Scheduling is one of the most important issues in the planning and operation of production systems. This paper investigates a general job shop scheduling problem with reentrant work flows and sequence dependent setup times. The disjunctive graph representation is used to capture the interactions between machines in job shop. Based on this representation, four two-phase heuristic procedures are proposed to obtain near optimal solutions for this problem. The obtained solutions in the first phase are substantially improved by reversing the direction of some critical disjunctive arcs of the graph in the second phase. A comparative study is conducted to examine the performance of these proposed algorithms.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.165-714
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• 2007

The basis number of a graph G is the least positive integer $k$ such that G has a $k$-fold basis. In this paper, we prove that the basis number of the cartesian product of a path with a circular ladder, a M$\ddot{o}$bius ladder and path with a net is exactly 3. This improves the upper bound of the basis number of these graphs for a general theorem on the cartesian product of graphs obtained by Ali and Marougi, see [2]. Also, by this general result, the cartesian product of a theta graph with a M$\ddot{o}$bius ladder is at most 5. But in section 3 we prove that it is at most 4.

• Nuclear Engineering and Technology
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• 제40권5호
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• pp.375-386
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• 2008

Conventional static reliability analysis methods are inadequate for modeling dynamic interactions between components of a system. Various techniques such as dynamic fault tree, dynamic Bayesian networks, and dynamic reliability block diagrams have been proposed for modeling dynamic systems based on improvement of the conventional modeling methods. In this paper, we review these methods briefly and introduce dynamic nodes to the existing reliability graph with general gates (RGGG) as an intuitive modeling method to model dynamic systems. For a quantitative analysis, we use a discrete-time method to convert an RGGG to an equivalent Bayesian network and develop a software tool for generation of probability tables.