• 대한수학회보
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• 제39권1호
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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.

• 대한수학회보
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• 제52권5호
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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.

• 대한수학회보
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• 제37권3호
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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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• 제42권1호
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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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• 제30권1호
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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.

• 대한수학회보
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• 제37권1호
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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)).

• 한국과학교육학회지
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• 제27권4호
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• pp.285-296
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• 2007

본 연구에서는 지구과학 그래프 유형을 분석하기 위한 기준을 만들고, 과학 교과서 비교 분석을 통하여 지구과학 그래프의 유형과 특징을 파악함으로써 지구과학 교과서에서 그래프의 기능과 구조에 대한 시사점을 얻고자 하였다. 지구과학 교과서 분석 결과, 선 그래프와 등치선도가 많이 사용되고 있는 것으로 나타났다. 선 그래프 중에는 단순 선 그래프 이외에도 다중 선 그래프와 YX 그래프의 사용 비율이 특히 높았다. 다른 과학 교과의 그래프와 비교 분석한 결과, 지구과학 교과는 다른 과학 교과에 비해 사용되는 그래프의 수가 많고 그 유형이 다양함을 알 수 있었다. 특히, 다른 과학 교과에 비해 선 그래프의 비율은 낮은 반면 등치선도, 분산 그래프 등의 비율이 높았다. 선 그래프 중에서는 특히 YX 그래프의 비율이 다른 교과에 비해 매우 높아 지구과학 교과의 가장 특정적인 그래프인 것으로 나타났다. 본 연구의 결과는 지구과학 교과서에서 그래프의 구조와 기능면에서의 개선을 시사하며, 학생들의 그래프 해석 능력에 대한 후속 연구를 제안한다.

• Korean Journal of Mathematics
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• 제31권4호
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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.

• 대한전자공학회논문지
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• 제6권3호
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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.

• 대한수학회논문집
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• 제30권2호
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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.