• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.487-491
• /
• 2000

Let G be a covering graph of G. We show that the line graph of G covers the line graph of G. Moreover, if the first covering is regular, then the line-graph covering is regular.

• Journal of The Korean Association For Science Education
• /
• v.25 no.6
• /
• pp.671-677
• /
• 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.

• Journal of The Korean Association For Science Education
• /
• v.25 no.2
• /
• pp.122-132
• /
• 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.

• Journal of The Korean Association For Science Education
• /
• v.26 no.1
• /
• pp.49-57
• /
• 2006

Line graphs are powerful tools in conveying complicated relationships and ideas because they show the relationship that exists between two continuous variables. Also, they can show readers the variations in variables and correlate two variables in a two dimensional space, and therefore, line graphs have a significant role in physics, especially kinematics. One of the purposes of the Test of Understanding Graphs in Kinematics (TUG-K) was to uncover student problems with interpreting kinematics. The TUG-K was given to Korean college students in 2004. To what extent are Korean college students able to understand such important line graphs? Analysis of the results of the TUG-K showed in which objectives students' strengths and weaknesses are found. This study investigates Korean college students' interpretation skills of kinematics graphs and the results of the study will be used to help instructors teach kinematics graphs more effectively.

• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.53-60
• /
• 2022

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and two distinct vertices x and y are adjacent if and only if x + y ∈ U(R), where U(R) denotes the set of units of R. In this paper, we find the commutative rings R for which G(R) is a line graph. Also, we find the rings for which the complements of unit graphs are line graphs.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1423-1431
• /
• 2015

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number is the minimum cardinality of a clique-transversal set in G. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.

• Journal of the military operations research society of Korea
• /
• v.27 no.1
• /
• pp.73-88
• /
• 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.

• East Asian mathematical journal
• /
• v.12 no.1
• /
• pp.71-76
• /
• 1996

• Journal of the Korean School Mathematics Society
• /
• v.23 no.3
• /
• pp.259-276
• /
• 2020

The purpose of this study was to identify how didactic transposition (teaching and learning methods) has occurred and developed in the teaching of graphs in elementary school mathematics textbooks for third and fourth graders according to the previous and current curricula. In this study, we analyzed the lesson units on bar graphs and line graphs in mathematics textbooks for each curriculum, from the fifth curriculum to the 2015 revised curriculum. We also investigated the implication of statistics education deriving from didactic transposition (teaching and learning methods). We found that the timing of teaching bar and line graphs was rarely changed as the curriculum has changed. In addition, the use of technology was not actively implemented in school statistics, although the curriculum emphasized the use of technology in statistical education. Lastly, the textbooks did not address the variability and distribution of data and the sample or sampling process, which are significant statistical concepts. Based on the findings of this study, we suggest how to teach statistical graphs and what to consider for the next mathematics textbook.

• Journal of The Korean Association For Science Education
• /
• v.27 no.4
• /
• pp.285-296
• /
• 2007

Graph is a major aspect of science textbooks. In this study, we investigated graph types and characteristics used in high school earth science subject by comparative analysis of science textbooks. The results of the analysis revealed that line graph and contour map was the most widely used graph types in earth science. Among line graphs, multiple line graph and YX graph was dominant. Comparing earth science graphs with other science graphs, earth science graphs exhibited superior in the number and variety. In earth science graphs, the portion of line graph was small, but the portion of contour map and scatter graph was larger than that of other science graphs. YX graph was the most specific graph type in earth science textbooks. The results of our study have implications for reform in function and structure of graph. We suggest that future studies be focused on students' ability of earth science graph interpretation.