• 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.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.159-167
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• 2024

The Topological indices are known as Mathematical characterization of molecules. In this paper, we have studied line graph of subdivision and semi-total point graph of triangular benzenoid, polynomino chains of 8-cycles and graphene sheet through forgotten and first Zagreb indices.

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

• 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.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• 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.

• 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.