• Proceedings of the KIEE Conference
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• 2000.11b
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• pp.389-391
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• 2000

A representation technique of a given track topology is required by many software applications in railway technology such as signalling system simulator. To achieve these, the concept of double vertex graph architecture is proposed. These are composed of pairs of vertices and node between the single vertices. Double vertex graph architecture can be understood as a extension of classical graphs. In developed railway signalling simulation software, it is shown that track topology can be represented by proposed algorithm in a efficient way. Especially it makes sure that these are suitable technique for representing and implementing of switch, routes which can be introduced some mistake in classical graph algorithm.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.363-377
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• 2015

Let R be a ring, (S,${\leq}$) a strictly ordered monoid and ${\omega}$ : S ${\rightarrow}$ End(R) a monoid homomorphism. The skew generalized power series ring R[[S,${\omega}$]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper, we investigate the interplay between the ring-theoretical properties of R[[S,${\omega}$]] and the graph-theoretical properties of its zero-divisor graph ${\Gamma}$(R[[S,${\omega}$]]). Furthermore, we examine the preservation of diameter and girth of the zero-divisor graph under extension to skew generalized power series rings.

• 전기의세계
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• v.22 no.4
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• pp.25-29
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• 1973

The computation of transmittances between arbitrary input and output nodes is of particular interest in the signal flow graph theory imput. The signal flow matrix [T] can be defined by [X]=-[T][X] where [X] and [Y] are input nose and output node matrices, respectively. In this paper, the followings are discussed; 1) Reduction of nodes by reforming the signal flow matrix., 2) Solution of input-output relationships by means of Gauss-Jordan reduction method, 3) Extension of the above method to the matrix signal flow graph.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.83-93
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• 2006

A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper, by characterizing the circuit graphs and investigating the structure of LV-graphs, we extend his result to 3-connected infinite locally finite VAP-free plane graphs.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.577-580
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• 2021

For a finite simplicial graph 𝚪, let G(𝚪) denote the right-angled Artin group on the complement graph of 𝚪. For path graphs P_k, cycle graphs C_ℓ and complete bipartite graphs K_n,m, this article characterizes the embeddability of G(K_n,m) in G(P_k) and in G(C_ℓ).

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.264-273
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• 2002

This paper focuses on disassembly sequencing, which is the problem of determining the optimum disassembly level and the corresponding disassembly sequence for a product at its end-of-life with the objective of maximizing the overall profit. In particular, sequence-dependent operation times, which frequently occur in practice due to tool-changeover, part reorientation, etc, are considered in the parallel disassembly environment. To represent the problem, a modified directed graph of assembly states is suggested as an extension of the existing extended process graph. Based on the directed graph, the problem is transformed into the shortest path problem and formulated as a linear programming model that can be solved straightforwardly with standard techniques. A case study on a photocopier was done and the results are reported.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.528-531
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• 2001

Finding a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges fuzzy weights can be used instead of crisp weights. and Type-2 fuzzy weight will be more suitable of this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type 2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.513-522
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• 1994

A multi-dimensional design is most easily constructed via the amalgamation of one-dimensional component block designs. However, not all sets of component designs are compatible to be amalgamated. The conditions for compatibility are related to the concept of a complete matching in a graph. In this paper, we give sufficient conditions for unequal-replicate designs. Two types of conditions are proposed; one is based on the number of verices adjacent to at least one vertex and the other is ona a degree of vertex, in a bipartite graph. The former is an extension of the sufficient conditions of equal-replicate designs given by Dean an Lewis (1988).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.314-318
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• 2001

Constructing a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges, fuzzy weights can be used instead of crisp weights, and Type-2 fuzzy weights will be more suitable if this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type-2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.