• 호남수학학술지
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• 제36권2호
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• pp.399-415
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• 2014

We study the Seifert surfaces of a link by relating the embeddings of graphs with induced graphs. As applications, we prove that every link L is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph $K_{2,n}$, where all voltage assignments on the edges of $K_{2,n}$ are 0. We also provide an algorithm to construct such a graph diagram of a given link and demonstrate the algorithm by dealing with the links $4^2_1$ and $5_2$.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.329-336
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• 1998

The class of doubly chordal graphs is a subclass of chordal graphs and a superclass of strongly chordal graphs which arise in so many application areas. Many optimization problems like domination and Steiner tree are NP-complete on chordal graps but can be solved in polynomial time on doubly chordal graphs. The central to designing efficient algorithms for doulby chordal graphs is the concept of (canonical)doubly perfect elimination orderings. We present linear time algorithms to compute a (canonical) double perfect elimination ordering of a doubly chordal graph.

• 대한수학회지
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• 제50권6호
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• pp.1199-1211
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• 2013

We introduce a new class of graphs, called quasi $m$-Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices. We determine when these graphs are strongly regular, and this leads us to define a new algebro-combinatorial structure, called quasi-partial difference family, or QPDF for short. We give several infinite families and sporadic examples of QPDFs. We also study several properties of QPDFs and determine, under several conditions, the form of the parameters of QPDFs when the group G is cyclic.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.555-569
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• 1999

The graph unit(chapter) is a good example of a topic in elementary school mathematics for which computer use can be incorporated as part of the instruction. Teaching graph can be facilitated by using the graphing utilities of computers, which make it possible to observe the property of many types of graphs. This study was concerned with utilizing an educational software Graphers as an instructional tool in teaching to help young students gain a better understanding of graph concepts. For this purpose, three types of instructional activities using Graphers were shown in the paper. Graphers is a data-gathering tool for creating pictorial data chosen from several data sets. They can represent their data on a table or with six types of graphs such as Pictograph, Bar Graph, Line Graph, Circle Graph, Grid Plot and Loops. They help students to select the graph(s) which are the most appropriate for the purpose of analyzing data while comparing various types of graphs. They also let them modify or change graphs, such as adding grid lines, changing the axis scale, or adding title and labels. Eventually, students have a chance to interpret graphs meaningfully and in their own way.

• 한국국방경영분석학회지
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• 제27권1호
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• pp.73-88
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• 2001

Designing high quality products and processes at a low cost is central technological and economic challenge to the engineer. The combination of engineering concepts and statistical implementations offered by Taguchi\`s off-line design technique has proven t be invaluable. By examining some deficiencies in designs from the Taguchi\`s highly fractional, orthogonal main effect plan based on orthogonal arrays, alternative method is proposed. The maximum resolution or the minimum aberration criterion is commonly used for selecting 2$^{n-m}$ fractional designs. We present new high resolution (low aberration) linear graphs to simplify the complexity of selecting designs with desirable statistical properties. The new linear graphs approach shows a substantial improvement over Taguchi\`s linear graphs and other related graphical methods for planning experiment. The new set of linear graphs will allow the experimenter to maintain the simple approach suggested by Taguchi while obtaining the best statistical properties of the resulting design such as minimum aberration as a by-product without dependency on complicated computational algorithm or additional statistical training.g.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권6호
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• pp.1620-1634
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• 2023

This paper studies the task of embedding nodes with multiple graphs representing multiple information channels, which is useful in a large volume of network clustering tasks. By learning a node using multiple graphs, various characteristics of the node can be represented and embedded stably. Existing studies using multi-channel networks have been conducted by integrating heterogeneous graphs or limiting common nodes appearing in multiple graphs to have similar embeddings. Although these methods effectively represent nodes, it also has limitations by assuming that all networks provide the same amount of information. This paper proposes a method to overcome these limitations; The proposed method gives different weights according to the source graph when embedding nodes; the characteristics of the graph with more important information can be reflected more in the node. To this end, a novel method incorporating a multi-channel gate layer is proposed to weigh more important channels and ignore unnecessary data to embed a node with multiple graphs. Empirical experiments demonstrate the effectiveness of the proposed multi-channel-based embedding methods.

• 대한수학회지
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• 제54권3호
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• 대한수학회보
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• 제55권5호
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• pp.1397-1404
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• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• 한국초등수학교육학회지
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• 제23권2호
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• pp.247-272
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• 2019

본 연구의 목적은 우리나라 초등수학 교육과정에 따른 통계영역의 그래프 지도를 분석하는 것이다. 이를 위해 다음과 같이 세 가지 연구문제를 설정하였다. 첫째, 초등수학 교육과정에서 그래프 지도와 관련된 성취기준의 변화는 어떠한가? 둘째, 초등수학 교육과정에서 그래프 그리기 지도의 변화는 어떠한가? 셋째, 초등수학 교육과정에서 그래프 이해 지도의 변화는 어떠한가? 첫 번째 연구문제를 위해 1차 교육과정부터 현행 2015 개정 교육과정의 통계영역의 지도와 관련된 성취기준을 분석하였다. 두 번째 연구문제를 위해 그래프 그리기를 지도할 때 학생들에게 그래프 그리는 기회를 얼마나 제공하는지(그리기 횟수)와 그래프의 기본틀을 제시하는지 여부(틀 제공)를 조사하였다. 세 번째 연구문제를 위해 교과서의 질문을 그래프 이해의 지도와 관련된 '자료 읽기', '자료 사이의 관계 찾기', '자료 해석하기', '상황 이해하기'로 구분하여 분석하였다. 분석 결과 교육과정에서 성취기준은 통계적 사고를 함양시키는 방향으로 변화하였으며, 그래프 그리기 지도를 쉽게 할 수 있도록 하고 그래프의 해석을 강조하는 방향으로 변화하고 있었다. 그러나 '자료해석하기'와 '상황이해하기'는 여전히 부족한 것으로 나타났다.

• 한국과학교육학회지
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• 제25권2호
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• pp.122-132
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• 2005

선 그래프는 막대그래프와 달리 각 변인들의 변화에 기인한 경향을 보여준다. 따라서 선 그래프로부터 경향을 파악할 수 있는지의 여부는 중요하다. 본 연구의 목적은 선 그래프 도식을 지닌 학생들이 선 그래프를 읽고 해석할 때 선 그래프 도식을 지니지 못한 학생들과 비교하여 어떠한 사고과정을 거치는지 파악하는 것이다. 발성사고를 통하여 고등학생틀의 선 그래프 이해 수준과 선 그래프 유형에 따라 선 그래프를 읽는 사고 과정의 특징을 분석한 결과, 동일하게 주어진 시간 동안에 상위 그룹에 해당하는 학생들은 하위 그룹에 속하는 학생들보다 더 많은 문장을 발성사고하였으며, 하위 그룹의 학생들과 달리 적응단계에서 선 그래프의 유형, 경향, 라벨 등을 파악하는데 오랜 시간을 사용하였다. 또한 상위그룹의 학생들은 하위그룹의 학생들보다 초인지적인 문장을 발성사고하는 경우가 더 많았다. 선 그래프 도식을 지닌 학생들과 단순히 일반적인 그래프 도식을 지닌 학생들을 구별하고 그에 따라 정보를 전달하는 방식을 달리하는 융통성이 필요하다.