• Title/Summary/Keyword: line graph

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Using of Scattering Bond Graph Methodology for a Physical Characteristics Analysis of “D-CRLH” Transmission Line

  • Taghouti, Hichem;Jmal, Sabri;Mami, Abdelkader
    • Journal of Electrical Engineering and Technology
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    • v.11 no.4
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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).

Analysis of Interpretation Processes Through Readers' Thinking Aloud in Science-Related Line Graphs (과학관련 선 그래프를 해석하는 고등학생들의 발성사고 과정 분석)

  • Kim, Tae-Sun;Kim, Beom-Ki
    • Journal of The Korean Association For Science Education
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    • v.25 no.2
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    • pp.122-132
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    • 2005
  • Graphing abilities are critical to understand and convey information in science. And then, to what extent are secondary students in science courses able to understand line graphs? To find clues about the students' interpretation processes of the information in science-related line graphs, this study has the following research question: Is there a difference between the levels of complexity of good and poor readers as they use the thinking aloud method for studying cognitive processes? The present study was designed to provide evidence for the hypothesis that good line graph readers use a specific graph interpretation process when reading and interpreting line graphs. With the aid of the thinking aloud method we gained deeper insight into the interpretation processes of good and poor graph readers while verifying verbal statements with respect to line graphs. The high performing students tend to read much more information and more trend-related information than the low performing students. We support the assumption of differential line graph schema existing in the high performing students in conjunction with general graph schema. Also, high performing students tend to think aloud much more metacognitively than low performing students. High performing students think aloud a larger quantity of information from line graphs than low performing students, and more trend-related sentences than value-related sentences from line graphs. The differences of interpretation processes revealed between good and poor graph readers while reading and interpreting line graphs have implications for instructional practice as well as for test development and validation. Teaching students to read and interpret graphs flexibly and skillfully is a particular challenge to anyone seriously concerned with good education for students who live in an technological society.

The Line n-sigraph of a Symmetric n-sigraph-V

  • Reddy, P. Siva Kota;Nagaraja, K.M.;Geetha, M.C.
    • Kyungpook Mathematical Journal
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    • v.54 no.1
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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.

ON THE ANNIHILATOR GRAPH OF GROUP RINGS

  • Afkhami, Mojgan;Khashyarmanesh, Kazem;Salehifar, Sepideh
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.1
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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.

MORE RELATIONS BETWEEN λ-LABELING AND HAMILTONIAN PATHS WITH EMPHASIS ON LINE GRAPH OF BIPARTITE MULTIGRAPHS

  • Zaker, Manouchehr
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.1
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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 Kn☐Kn and the generation of λ-squares.

ON CO-WELL COVERED GRAPHS

  • Abughazaleh, Baha';Abughneim, Omar;Al-Ezeh, Hasan
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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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.

Using an educational software Graphers in elementary school mathematics (초등 수학 수업에서의 소프트웨어(Graphers) 활용)

  • 황혜정
    • School Mathematics
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    • v.1 no.2
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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.

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Interpretation Abilities of American and Korean Students in Kinematics Graphs

  • Kim, Tae-Sun;Kim, Ji-Na;Kim, Beom-Ki
    • Journal of The Korean Association For Science Education
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    • v.25 no.6
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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.

Analysis of Children's Constructing and Interpreting of a Line Graph in Science (초등학생들의 과학 선 그래프 작성 및 해석 과정 분석)

  • Yang, Su Jin;Jang, Myoung-Duk
    • Journal of Korean Elementary Science Education
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    • v.31 no.3
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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.

SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p3

  • Darafsheh, Mohammad Reza;Shahsavaran, Mohsen
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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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.