• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.475-491
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• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.103-110
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• 2005

This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

• School Mathematics
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• v.18 no.1
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• pp.127-141
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• 2016

This study analyzes modes related to use of graph representation that appears to solve high school students quadratic function problem based on the graph using modes of Chauvat. It was examined the extent of understanding of the quadratic function of students through the flexibility of the representation of the Bannister (2014) from the analysis. As a result, the graph representation mode in which a high school students are mainly used is a nomographic specific mode, when using operational mode, it was found to be an error. The flexibility of Bannister(2014) that were classified to the use of representation from the point of view of the object and the process in the understanding of the function was constrained operation does not occur between the two representations in understanding the function in the process of perspective. Based on these results, the teaching on use graph representation for the students in classroom is required and the study of teaching and learning methods can understand the function from various perspectives is needed.

• The Journal of Korea Robotics Society
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• v.9 no.3
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• pp.178-184
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• 2014

Tendon driven robot mechanisms have many advantages such as allowing miniaturization and light-weight designs and/or enhancing flexibility in the design of structures. When designing or analyzing tendon driven mechanisms, it is important to determine how the tendons should be connected and whether the designed mechanism is easily controllable. Graph representation is useful to view and analyze such tendon driven mechanisms that are complicatedly interconnected between mechanical elements. In this paper, we propose a method of generalized graph representation that provides us with an intuitive analysis tool not only for tendon driven manipulators, but also various other kinds of mechanical systems which are combined with tendons. This method leads us to easily obtain structure matrix - which is the one of the most important steps in analyzing tendon driven mechanisms.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.37-45
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• 2002

We described a method of resonant mode identification in dielectric-disc loaded cylindrical cavity resonators. The characteristic equations are solved using the ContourPlot graph of Mathematica. Contour graph method uses graphical method. It is comparable with numerical method. The numerical method is very difficult mode identification. The analysis is based on the approximated electromagnetic representation which is only concentrated on the calculation of resonant frequencies, and a mode identification of resonant frequencies has not been covered. However, It is possible to calculate precise resonant frequencies and to identify the mode of resonant frequencies using the contour graph method. The contour graph method is not a method using approximated representation of electromagnetic field variation at the outer area of dielectric in the resonators. It is a method using enact representation.

• The Journal of Korea Robotics Society
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• v.19 no.2
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• pp.196-202
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• 2024

The ability to understand given environments and plan a sequence of actions leading to goal state is crucial for personal service robots. With recent advancements in deep learning, numerous studies have proposed methods for state representation in planning. However, previous works lack explicit information about relationships between objects when the state observation is converted to a single visual embedding containing all state information. In this paper, we introduce graph-based state representation that incorporates both object and relationship features. To leverage these advantages in addressing the task planning problem, we propose a Graph Neural Network (GNN)-based subgoal prediction model. This model can extract rich information about object and their interconnected relationships from given state graph. Moreover, a search-based algorithm is integrated with pre-trained subgoal prediction model and state transition module to explore diverse states and find proper sequence of subgoals. The proposed method is trained with synthetic task dataset collected in simulation environment, demonstrating a higher success rate with fewer additional searches compared to baseline methods.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.238-246
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• 2011

This paper proposes a new semantic representation and its associated similarity measure. The representation expresses textual context observed in a context of a certain term as a network where nodes are terms and edges are the number of cooccurrences between connected terms. To compare terms represented in networks, a graph kernel is adopted as a similarity measure. The proposed representation has two notable merits compared with previous semantic representations. First, it can process polysemous words in a better way than a vector representation. A network of a polysemous term is regarded as a combination of sub-networks that represent senses and the appropriate sub-network is identified by context before compared by the kernel. Second, the representation permits not only words but also senses or contexts to be represented directly from corresponding set of terms. The validity of the representation and its similarity measure is evaluated with two tasks: synonym test and unsupervised word sense disambiguation. The method performed well and could compete with the state-of-the-art unsupervised methods.

• The Mathematical Education
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• v.13 no.2
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• pp.6-10
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• 1974

We consider 'ordinary' graphs: that is, finite undirected graphs with no loops or multiple edges. An intersection representation of a graph G is a function r from V(G), the set of vertices of G, into a family of sets S such that distinct points $\chi$$_{\alpha}$ and $\chi$$_{\beta}$/ of V(G) are. neighbors in G precisely when ${\gamma}$($\chi$$_{\alpha}$)∩${\gamma}$($\chi$$_{\beta}$/)$\neq$ø, A graph G is a rigid circuit grouph if every cycle in G has at least one triangular chord in G. In this paper we consider the main theorem; A graph G has an intersection representation by arcs on an acyclic graph if and only if is a normal rigid circuit graph.uit graph.d circuit graph.uit graph.

• The Transactions of the Korea Information Processing Society
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• v.5 no.10
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• pp.2567-2574
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• 1998

Many software engineering tools and techniques rely on fraphic representations of software, such as control flow graphs, program dependene graphs, or system dependence graphs. Existing graphic representations for object-oriented programs are compkicated, reduplicated. We thus propose a new graphic representation for object-oriented programs. Object-oriented Program Dependency Graph (OPDG). An OPDG consists of class dependence graph, class hierarchy graph and procedure dependence graph. Other features of OPDG are (1) the representation is compact; (2) the representation is easy to extend for the incremental development of a program; and (3) the repreesentation can be extended to provide dynamic information.

• The Mathematical Education
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• v.58 no.3
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• pp.403-422
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• 2019

As the informal graph was introduced newly in the area of function in middle school mathematics curriculum revised in 2015, ten publishing company became to have a concern on how to represent the graph content uniquely and newly. At this time, it may be meaningful and useful to compare and analyze the content of the graph unit shown on each textbook published by publishing companies. To accomplish this, on fundamentally the basis of diverse prior researches this study tried to select the elements of expression and interpretation of the graph and establish an analytic frameworks of expression and interpretation of the graph respectively. This study executed the frequency analysis and cross analysis by textbook system, textbook, and the number of the graph drawn on a coordinate plane on the representation and interpretation of the graph. As a result, the textbook contains more items on interpretation than the representation of the graph, and students showed a learning effect on the graph unit but showed a neutral response to the impact of learning. This basic and essential paper shed light on developing the practical and more creative textbook which has diversity and characteristic respectively, while adjusting the scope of the elements of the graph's representations and interpretations and providing proper level and quality content.