• Journal of Information Technology Applications and Management
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• v.19 no.1
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• pp.13-24
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• 2012

Usability and knowledge drawn from utilizing various ways of representing accounting data were examined. Classroom experiments were conducted to compare students' assessment of financial data using table of numbers, 2-dimensional column graphs (2D), 3-dimensional column graphs (3D), and mixed reality visualization of true 3-dimensional graphs (MR). The results showed that in assessing the financial status and performance of a firm, Table of numbers and MR took longer than 2D and 3D graphs. The time spent on true 3D graphs using MR technology was about the same as Table of numbers. When compared the assessment scores of the firm's financial status and performance between participants and experts, the difference was the least when participants used 2D graphs. However, MR was seen as being a new way to provide data of greater complexity and was very useful for financial information.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• The Journal of Korean Institute for Practical Engineering Education
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• v.2 no.2
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• pp.49-54
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• 2010

The functions and their graphs are very important parts in mathematical educations. But there seems be a lot of students studying the functions and their graphs without grasping the meaning of them and without interest with them. We present a learning method of how to match functions and their graphs with outlines of various shapes. That is, outlines of the shapes are assumed to be the graphs of the functions and the graphs will be plotted on the screen of a computer with help of the computer algebra system.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.125-140
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• 2006

Let $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ be the number of general4-regular graphs on n labelled vertices with $l_1+2l_2$ loops, d double edges, t triple edges and q quartet edges. We use inclusion and exclusion with five types of properties to determine the asymptotic behavior of $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ and hence that of g(2n), the total number of general 4-regular graphs where $l_1,\;l_2,\;d,\;t\;and\;q\;=\;o(\sqrt{n})$, respectively. We show that almost all general 4-regular graphs are 2-connected. Moreover, we determine the asymptotic numbers of general 4-regular graphs with given connectivities.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.311-335
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• 2024

The fundamental quandle is a powerful invariant of knots, links and spatial graphs, but it is often difficult to determine whether two quandles are isomorphic. One approach is to look at quotients of the quandle, such as the n-quandle defined by Joyce [8]; in particular, Hoste and Shanahan [5] classified the knots and links with finite n-quandles. Mellor and Smith [12] introduced the N-quandle of a link as a generalization of Joyce's n-quandle, and proposed a classification of the links with finite N-quandles. We generalize the N-quandle to spatial graphs, and investigate which spatial graphs have finite N-quandles. We prove basic results about N-quandles for spatial graphs, and conjecture a classification of spatial graphs with finite N-quandles, extending the conjecture for links in [12]. We verify the conjecture in several cases, and also present a possible counterexample.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1069-1073
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• 1997

We characterize supersolvable signed graphs by using simplicial nodes and some signed graphs $\Delta_2, L_k$.

• Journal of KIISE
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• v.43 no.10
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• pp.1131-1143
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• 2016

How can we effectively compress big graphs composed of billions of edges? By concentrating non-zeros in the adjacency matrix through vertex rearrangement, we can compress big graphs more efficiently. Also, we can boost the performance of several graph mining algorithms such as PageRank. SlashBurn is a state-of-the-art vertex rearrangement method. It processes real-world graphs effectively by utilizing the power-law characteristic of the real-world networks. However, the original SlashBurn algorithm displays a noticeable slowdown for large-scale graphs, and cannot be used at all when graphs are too large to fit in a single machine since it is designed to run on a single machine. In this paper, we propose a distributed SlashBurn algorithm to overcome these limitations. Distributed SlashBurn processes big graphs much faster than the original SlashBurn algorithm does. In addition, it scales up well by performing the large-scale vertex rearrangement process in a distributed fashion. In our experiments using real-world big graphs, the proposed distributed SlashBurn algorithm was found to run more than 45 times faster than the single machine counterpart, and process graphs that are 16 times bigger compared to the original method.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.119-141
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• 2019

This study was carried out in order to draw some implications for teaching statistical graph in mathematics education with respect to practical statistics education for promoting students' statistical literacy. We analyze 133 graphs appearing in 99 elementary textbooks of other subjects (subjects except from mathematics) by subjects and types, and identify some cases of graphs addressed by other subjects. As a results, statistical graph was most addressed in social studies, and bar graphs, line graphs, tables, and circle graphs are most used in other subjects. Moreover, there are some issues related to contents-(1) the problem of curricular sequencing between mathematics and other subjects, (2) the level of addressing ratio graph, and (3) the use of wavy lines. In terms of forms, (1) the visual variation of graphical representations, (2) representation combining multiple graphs, and (2) graphs specialized for particular subjects are drawn as other issues. We suggest some implications to be considered when teaching the statistical graph in elementary mathematics classes.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of Information Processing Systems
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• v.16 no.6
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• pp.1407-1423
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• 2020

A graph is a data structure consisting of nodes and edges between these nodes. Graph embedding is to generate a low dimensional vector for a given graph that best represents the characteristics of the graph. Recently, there have been studies on graph embedding, especially using deep learning techniques. However, until now, most deep learning-based graph embedding techniques have focused on unweighted graphs. Therefore, in this paper, we propose a graph embedding technique for weighted graphs based on long short-term memory (LSTM) autoencoders. Given weighted graphs, we traverse each graph to extract node-weight sequences from the graph. Each node-weight sequence represents a path in the graph consisting of nodes and the weights between these nodes. We then train an LSTM autoencoder on the extracted node-weight sequences and encode each nodeweight sequence into a fixed-length vector using the trained LSTM autoencoder. Finally, for each graph, we collect the encoding vectors obtained from the graph and combine them to generate the final embedding vector for the graph. These embedding vectors can be used to classify weighted graphs or to search for similar weighted graphs. The experiments on synthetic and real datasets show that the proposed method is effective in measuring the similarity between weighted graphs.