• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.527-535
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• 2021

The fundamental group of a high dimensional graph manifold canonically has a graph of groups structure. We analyze the group action on the associated Bass-Serre tree and study the algebraic ranks of the fundamental groups of high dimensional graph manifolds.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1753-1763
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• 2013

In this paper, we show that tree products of certain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.795-805
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• 2022

The aim of author's in this paper is to study the Cayley graph in the realm of signed graph. Moreover, we have characterized generating sets and finite abelian groups that corresponds to balanced Cayley signed graphs. The notion of Cayley signed graph has been demonstrated with the ample number of examples.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.349-361
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• 2012

CAT(0) cubical complexes are a key to formulate geodesic spaces with nonpositive curvatures. The paper discusses the median structure of CAT90) cubical complexes. Especially, the underlying graph of a CAT(0) cubical complex is a median graph. Using the idea of median structure, this paper shows that groups acting on median complexes L(${\delta}$) groups and, in addition, work L(0) groups are closed under free product.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.81-96
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• 2015

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if $H{\cap}K{\neq}1$ where 1 denotes the trivial subgroup of G. In this paper we characterize all finite groups whose intersection graphs are planar. Our methods are elementary. Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroup graph of a group, each of whose planarity was already considered before in [2, 10, 11, 12].

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1171-1213
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• 2023

This work is a continuation of Crisp's work on automorphism groups of CLTTF Artin groups, where the defining graph of a CLTTF Artin group is connected, large-type, and triangle-free. More precisely, we provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group whose defining graph has no separating vertices.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.399-426
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• 2018

Cofinite graphs and cofinite groupoids are defined in a unified way extending the notion of cofinite group introduced by Hartley. These objects have in common an underlying structure of a directed graph endowed with a certain type of uniform structure, called a cofinite uniformity. Much of the theory of cofinite directed graphs turns out to be completely analogous to that of cofinite groups. For instance, the completion of a directed graph Γ with respect to a cofinite uniformity is a profinite directed graph and the cofinite structures on Γ determine and distinguish all the profinite directed graphs that contain Γ as a dense sub-directed graph. The completion of the underlying directed graph of a cofinite graph or cofinite groupoid is observed to often admit a natural structure of a profinite graph or profinite groupoid, respectively.

• Kyungpook Mathematical Journal
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• v.45 no.4
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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.

• Journal of the Korean earth science society
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• v.31 no.4
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• pp.378-391
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• 2010

The purpose of this study was to investigate the graph interpretation ability and perception of high school students and preservice secondary teachers in Earth science. We developed two different instruments; one was a graph interpretation ability inventory that consists of 9 graph types with 18 items, and the other one is two questionnaires to explore the participants' perception about Earth science-related graph. The results of this study are as follows: High school students and preservice secondary teachers demonstrated their remarkable ability in interpreting a line graph, but showed their limited ability with the graph of overlapped and directional change, which means the graph interpretation ability was affected by a graph type; two groups participated in this study revealed a considerable difference in the graph interpretation ability depending on the grade level; preservice teachers were superior to high school students in discriminating two graphs, the representation method, which are different with the same topic; and many participants in both groups considered that the property of Earth science graph was considerably different from that of other science subjects, especially in directional change graph, scatter graph, contour map, and domain graph. The results suggest that the effective graph instruction strategies be developed in Earth science learning.