• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.531-539
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• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• Kyungpook Mathematical Journal
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• 제64권2호
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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.

• 한국컴퓨터정보학회논문지
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• 제23권12호
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• pp.57-64
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• 2018

In this paper, a method to measure similarity between two graphs is proposed, which is based on centralities of the graphs. The similarity between two graphs $G_1$ and $G_2$ is defined by the difference of distance($G_1$, $G_{R_1}$) and distance($G_2$, $G_{R_2}$), where $G_{R_1}$ and $G_{R_2}$ are set of random graphs that have the same number of nodes and edges as $G_1$ and $G_2$, respectively. Each distance ($G_*$, $G_{R_*}$) is obtained by comparing centralities of $G_*$ and $G_{R_*}$. Through the computational experiments, we show that it is possible to compare graphs regardless of the number of vertices or edges of the graphs. Also, it is possible to identify and classify the properties of the graphs by measuring and comparing similarities between two graphs.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

• Journal of Multimedia Information System
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• 제3권3호
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• pp.53-61
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• 2016

This research proposes the index optimization as a classification task and application of the graph based KNN. We need the index optimization as an important task for maximizing the information retrieval performance. And we try to solve the problems in encoding words into numerical vectors, such as huge dimensionality and sparse distribution, by encoding them into graphs as the alternative representations to numerical vectors. In this research, the index optimization is viewed as a classification task, the similarity measure between graphs is defined, and the KNN is modified into the graph based version based on the similarity measure, and it is applied to the index optimization task. As the benefits from this research, by modifying the KNN so, we expect the improvement of classification performance, more graphical representations of words which is inherent in graphs, the ability to trace more easily results from classifying words. In this research, we will validate empirically the proposed version in optimizing index on the two text collections: NewsPage.com and 20NewsGroups.

• 한국컴퓨터정보학회논문지
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• 제24권7호
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• pp.61-69
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• 2019

In this paper, a classification method of random graph models is proposed and it is based on centralities of the random graphs. Similarity between two random graphs is measured for the classification of random graph models. The similarity between two random graph models $G^{R_1}$ and $G^{R_2}$ is defined by the distance of $G^{R_1}$ and $G^{R_2}$, where $G^{R_2}$ is a set of random graph $G^{R_2}=\{G_1^{R_2},...,G_p^{R_2}\}$ that have the same number of nodes and edges as random graph $G^{R_1}$. The distance($G^{R_1},G^{R_2}$) is obtained by comparing centralities of $G^{R_1}$ and $G^{R_2}$. Through the computational experiments, we show that it is possible to compare random graph models regardless of the number of vertices or edges of the random graphs. Also, it is possible to identify and classify the properties of the random graph models by measuring and comparing similarities between random graph models.

• 전자공학회논문지B
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• 제33B권10호
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• pp.120-129
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• 1996

This paper presents an efficient block segmentation and classification using the edge information of the document image. We extract four prominent features form the edge gradient and orientaton, all of which, and thereby the block clssifications, are insensitive to the background noise and the brightness variation of of the image. Using these four features, we can efficiently classify a document image into the seven categrories of blocks of small-size letters, large-size letters, tables, equations, flow-charts, graphs, and photographs, the first five of which are text blocks which are character-recognizable, and the last two are non-character blocks. By introducing the clumn interval and text line intervals of the document in the determination of th erun length of CRLA (constrained run length algorithm), we can obtain an efficient block segmentation with reduced memory size. The simulation results show that the proposed algorithm can rigidly segment and classify the blocks of the documents into the above mentioned seven categories and classification performance is high enough for all the categories except for the graphs with too much variations.

• 대한수학회보
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• 제57권3호
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• pp.739-750
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• 2020

A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p² exists. In this paper an extension of his result in the case of cubic graphs of order 34p³, p ≠ 17, is obtained.

• Journal of Information Processing Systems
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• 제13권6호
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• pp.1554-1574
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• 2017

This paper introduces a new type of determining factor for Pseudo Random Strings (PRS). This classification depends upon a mathematical property called Finite Induction (FI). FI is similar to a Markov Model in that it presents a model of the sequence under consideration and determines the generating rules for this sequence. If these rules obey certain criteria, then we call the sequence generating these rules FI a PRS. We also consider the relationship of these kinds of PRS's to Good/deBruijn graphs and Linear Feedback Shift Registers (LFSR). We show that binary sequences from these special graphs have the FI property. We also show how such FI PRS's can be generated without consideration of the Hamiltonian cycles of the Good/deBruijn graphs. The FI PRS's also have maximum Shannon entropy, while sequences from LFSR's do not, nor are such sequences FI random.

• 한국음향학회지
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• 제43권2호
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• pp.234-242
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• 2024

본 논문에서는 그래프 신경망을 이용한 수동소나 신호 분류 알고리즘을 제안한다. 제안하는 알고리즘은 스펙트로그램을 영상 패치로 분할하고, 인접 거리의 영상 패치 간 연결을 통해 그래프를 표현한다. 이후, 표현된 그래프를 이용하여 그래프 합성곱 신경망을 학습하고 신호를 분류한다. 공개된 수중 음향 데이터를 이용한 실험에서 제안된 알고리즘은 스펙트로그램의 선 주파수 특징을 그래프 형태로 표현하며, 92.50 %의 우수한 분류 정확도를 갖는다. 이러한 결과는 기존의 합성곱 신경망과 비교하여 8.15 %의 높은 분류 정확도를 갖는다.