• Journal of Electrical Engineering and Technology
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• 제11권4호
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• pp.943-950
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• 2016

In this paper, we propose to analyze the physical characteristics of a planar dual-composite right-left handed transmission line by a common application of Bond Graph approach and Scattering formalism (Methodology S.BG). The technique, we propose consists, on the one hand, of modeling of a dual composite right-left metamaterial transmission line (D-CRLH-TL) by Bond Graph approach, and, it consists of extracting the equivalent circuit of this studied structure. On the other hand, it consists to exploiting the scattering parameters (Scattering matrix) of the DCRLH-TL using the methodology which we previously developed since 2009. Finally, the validation of the proposed and used technique is carried out by comparisons between the simulations results with ADS and Maple (or MatLab).

• 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.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• 대한수학회보
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• 제54권1호
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• pp.331-342
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• 2017

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for $a{\in}Z(R)$, let $ann(a)=\{r{\in}R{\mid}ra=0\}$. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if $ann(xy){\neq}ann(x){\cup}ann(y)$. In this paper, we study the annihilator graph associated to a group ring RG.

• 대한수학회보
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• 제59권1호
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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.

• 대한수학회논문집
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• 제35권2호
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• pp.359-370
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• 2020

A graph G is called a well covered graph if every maximal independent set in G is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.

• 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.

• 한국과학교육학회지
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• 제25권6호
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• pp.671-677
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• 2005

Line graphs are powerful tools in conveying complicated relationships and ideas because line graphs show the relationship that exists between two continuous variables. Also, line graphs can show readers the variations in variables and correlate two variables in a two dimensional space. For these reasons, line graphs have a significant role in physics, especially kinematics. To what extent are Korean college and secondary students able to understand kinematics graphs? Is there a difference between American students and Korean students in interpreting kinematics graphs? The TUG-K instrument (Test of Understanding Graphs in Kinematics) was administered to students in both countries. The results show the difference between American students and Korean students by TUG-K objective. Also, the results are discussed in terms of a graph comprehension theory.

• 한국초등과학교육학회지:초등과학교육
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• 제31권3호
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• pp.321-333
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• 2012

The purpose of this study was to examine elementary school students' characteristics and difficulties in drawing and interpreting a line graph, and to present educational implications. Twenty five students(4th grader: 6, 5th grader: 9, and 6th grader: 10) at an elementary school participated in this study. We used a student's task which was about graphing on a given data table and interpreting his/her graph. The data table was on heating 200mL and 500mL of water and measuring their temperature at regular time intervals. We collected multiple source of data, and data analyzed based on the sub-variables of TOGS. The some results of this study are as follows: First, five children (20.0%), especially two of 10 sixth graders (20.0%), could not construct a line graph about a given data table. Second, twenty students (80.0%) had the ability on 'Scaling axes' and on 'Assigning variables to the axes', however, only a student understood why the time is on the longitudinal axis and the temperature is on the vertical axis. Third, in the case of 'Plotting points', twelve children (48.0%) could drew two graphs on a coordinate. Fourth, in the case of 'Selecting the corresponding value for Y (or X)', twenty student had little difficulty. on 'Describing the relationship between variables', seventeen students (68.0%) understood the relationship between time and temperature of water, and the relationship between temperature and amount of water. Finally, eleven students (44%) had the ability on 'Interrelating and extrapolation graphs.' Educational implications are also presented in this paper.

• 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.