• 대한수학회보
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• 제52권2호
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• pp.467-481
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• 2015

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the $Poincar\acute{e}$ polynomial $P_{M(G)}(z)$, which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.531-540
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• 2008

We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.

• 한국과학교육학회지
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• 제25권6호
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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.

• 한국지능시스템학회논문지
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• 제24권4호
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• pp.430-436
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• 2014

행렬스타 그래프와 하프팬케익 그래프는 스타 그래프의 변형으로 노드 대칭성과 허용도 등 여러 가지 좋은 성질을 갖는다. 본 연구에서는 행렬스타 그래프와 하프팬케익 그래프 사이의 임베딩을 분석한다. 연구 결과로 행렬스타 그래프 $MS_{2,n}$는 하프팬케익 그래프 $HP_{2n}$에 연장율 5, 확장율 1에 임베딩 가능하다. 또한 하프팬케익 그래프 $HP_{2n}$는 행렬스타 그래프 $MS_{2,n}$에 임베딩하는 연장율 비용이 O(n)임을 보인다. 이러한 결과는 스타 그래프에서 개발된 여러 가지 알고리즘을 하프팬케익 그래프에서 상수의 추가적인 비용으로 시뮬레이션 할 수 있음을 의미한다. 왜냐하면 스타 그래프 $S_n$은 행렬스타 그래프 $MS_{2,n}$의 부분 그래프이기 때문이다.

• 대한수학회지
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• 제57권5호
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• pp.1103-1118
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• 2020

In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These multiarc graphs naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and topology. We show a number of rigidity results, namely showing that, under certain complexity conditions, that simplicial maps between them only arise in the "obvious way". We also observe that, again under necessary complexity conditions, subsurface strata are convex. Put together, these results imply that certain simplicial maps always give rise to convex images.

• 대한수학회보
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• 제38권2호
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• pp.317-324
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• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.577-580
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• 2021

For a finite simplicial graph 𝚪, let G(𝚪) denote the right-angled Artin group on the complement graph of 𝚪. For path graphs P_k, cycle graphs C_ℓ and complete bipartite graphs K_n,m, this article characterizes the embeddability of G(K_n,m) in G(P_k) and in G(C_ℓ).

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• 대한수학회보
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• 제56권4호
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• pp.1059-1075
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• 2019

Let G be a graph with no isolated vertex. A total dominating set, abbreviated TDS of G is a subset S of vertices of G such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a TDS of G. In this paper, we study the total domination number of central graphs. Indeed, we obtain some tight bounds for the total domination number of a central graph C(G) in terms of some invariants of the graph G. Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and complete multipartite graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of central graphs.

• 한국컴퓨터정보학회논문지
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• 제23권12호
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• pp.57-64
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• 2018

In this paper, a method to measure similarity between two graphs is proposed, which is based on centralities of the graphs. The similarity between two graphs $G_1$ and $G_2$ is defined by the difference of distance($G_1$, $G_{R_1}$) and distance($G_2$, $G_{R_2}$), where $G_{R_1}$ and $G_{R_2}$ are set of random graphs that have the same number of nodes and edges as $G_1$ and $G_2$, respectively. Each distance ($G_*$, $G_{R_*}$) is obtained by comparing centralities of $G_*$ and $G_{R_*}$. Through the computational experiments, we show that it is possible to compare graphs regardless of the number of vertices or edges of the graphs. Also, it is possible to identify and classify the properties of the graphs by measuring and comparing similarities between two graphs.