• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1091-1101
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• 2018

We concern in this paper the graph Kazdan-Warner equation $${\Delta}f=g-he^f$$ on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h{\leq}0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.959-962
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• 2002

This paper presents a method of constructing the universal multiple processing element unit(UMPEU) based on De Bruijn Graph. The proposed method is as following. Firstly we propose transformation operators in order to construct the De Bruijn graph using properties of graph. Secondly we construct the transformation table of De Bruijn graph using above transformation operators. Finally we construct the De Bruijn graph using transformation table. The proposed UMPEU is capable of constructing the De Bruijn geraph for any prime number and integer value of finite fields. Also the UMPEU is applied to fault-tolerant computing system, pipeline class, parallel processing network, switching function and its circuits.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.369-380
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• 2010

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.851-860
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• 2008

A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.27-40
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• 2002

For two integers m, n with m $\leq$ n, an [m,n]-factor F in a graph G is a spanning subgraph of G with m $\leq$ d$\_$F/(v) $\leq$ n for all v ∈ V(F). In 1996, H. Enomoto et al. proved that every 3-connected Planar graph G with d$\_$G/(v) $\geq$ 4 for all v ∈ V(G) contains a [2,3]-factor. In this paper. we extend their result to all 3-connected locally finite infinite planar graphs containing no unbounded faces.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.06e
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• pp.129-132
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• 1998

A bond graph modeling approach which is equivalent to a finite element method is formulated in the case of the piezoelectric thickness vibrator. This formulation suggests a new definition of the generalized displacements for a continuous system as well as the piezoelectric thickness vibrator. The newly defined coordinates are illustrated to be easily interpreted physically and easily used in analysis of the system performance. The bond graph model offers the primary advantage of physical realizability and has a greater physical accuracy because of the use of multiport energic elements. While results are presented is general in scope and can be applied to arbitrary physical systems.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.497-505
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• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.197-201
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• 2014

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.