• Title, Summary, Keyword: line graph

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CELLULAR EMBEDDINGS OF LINE GRAPHS AND LIFTS

  • Kim, Jin-Hwan
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.175-184
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    • 2002
  • A Cellular embedding of a graph G into an orientable surface S can be considered as a cellular decomposition of S into 0-cells, 1-cells and 2-cells and vise versa, in which 0-cells and 1-cells form a graph G and this decomposition of S is called a map in S with underlying graph G. For a map M with underlying graph G, we define a natural rotation on the line graph of the graph G and we introduce the line map for M. we find that genus of the supporting surface of the line map for a map and we give a characterization for the line map to be embedded in the sphere. Moreover we show that the line map for any life of a map M is map-isomorphic to a lift of the line map for M.

CLIQUE-TRANSVERSAL SETS IN LINE GRAPHS OF CUBIC GRAPHS AND TRIANGLE-FREE GRAPHS

  • KANG, LIYING;SHAN, ERFANG
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1423-1431
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    • 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.

LINE GRAPHS OF COVERING GRAPHS ARE COVERING GRAPHS

  • Dan Archdeacon;Lee, Jaeun;Sohn, Moo-Young
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.487-491
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    • 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.

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Analysis of Graph Types and Characteristics Used in Earth Science Textbooks (지구과학 교과서에 사용된 그래프의 유형 및 특징 분석)

  • Lee, Jin-Bong;Lee, Ki-Young
    • Journal of The Korean Association For Science Education
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    • v.27 no.4
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    • pp.285-296
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    • 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.

MATCHINGS IN LINE GRAPHS

  • Nam, Yun-Sun
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.121-125
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    • 2000
  • In this paper, we obtain an algorithm for finding a maximum matching in the line graph L(G) of a graph G. The complexity of our algorithm is O($$\mid$E$\mid$$), where is the edge set of G($$\mid$E$\mid$$ is equal to the number of vertices in L(G)).

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Analysis on Signal Flow Graph of Slotted LIne (Slotted Line의 Signal Flow Graph 해석)

  • 박기수
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.6 no.3
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    • pp.8-11
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    • 1969
  • In the precision measurement of the voltage standing wave ratio (VSWR) or reflection coefficient by means of the slotted line technique, one of the important factors is the maximum error due to the discontinuities and multi-reflection in the slotted line. Particularly, this error becomes a critical factor when the VSWR or the reflection coefficient to be measured is very small. In this paper, the exact expression of this error is obtained by means of the Signal flow graph method.

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MINIMUM RANK OF THE LINE GRAPH OF CORONA CnoKt

  • Im, Bokhee;Lee, Hwa-Young
    • Communications of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.65-72
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    • 2015
  • The minimum rank mr(G) of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose (i, j)-th entry (for $i{\neq}j$) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The corona $C_n{\circ}K_t$ is obtained by joining all the vertices of the complete graph $K_t$ to each n vertex of the cycle $C_n$. For any t, we obtain an upper bound of zero forcing number of $L(C_n{\circ}K_t)$, the line graph of $C_n{\circ}K_t$, and get some bounds of $mr(L(C_n{\circ}K_t))$. Specially for t = 1, 2, we have calculated $mr(L(C_n{\circ}K_t))$ by the cut-vertex reduction method.

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).

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.

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.