• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.893-908
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• 2010

In this paper we prove the existence of spanning 3-trees in a 3-connected infinite locally finite VAP-free plane graph. Together with the results of Barnette and the author, this yields that every finite or infinite 3-connected locally finite VAP-free plane graph contains a spanning 3-tree.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.655-665
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• 2014

The number of topologies (non-homeomorphic topologies) on a fixed finite set having n elements are now known up to n = 18 (n = 16 respectively) but still no complete formula yet. There are one to one correspondences among topologies, preorders and transitive digraphs on a given finite set. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite simple graph.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.625-647
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• 2002

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1405-1417
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• 2018

The aim of this work is to introduce several different volume computational methods of graph polytopes associated with various types of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.

• 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.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.531-539
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• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.969-975
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• 2022

Let R be a finite commutative ring with nonzero unity and let Z(R) be the zero divisors of R. The total graph of R is the graph whose vertices are the elements of R and two distinct vertices x, y ∈ R are adjacent if x + y ∈ Z(R). The total graph of a ring R is denoted by 𝜏(R). The independence number of the graph 𝜏(R) was found in [11]. In this paper, we again find the independence number of 𝜏(R) but in a different way. Also, we find the independent dominating number of 𝜏(R). Finally, we examine when the graph 𝜏(R) is well-covered.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.183-191
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• 2017

We define a stratification and a partition of a finite topological space and define a partial order on the partition. Open subsets can be described completely in terms of this partially ordered partition. We associate a directed graph to the partially ordered partition of a finite topological space. This gives a one-to-one correspondence between finite topological spaces and a certain class of directed graphs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.9
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• pp.1965-1970
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• 2011

This paper proposes the method of switching function implementation using switching function extraction based on graph over finite fields. After we deduce the matrix equation from path number of directional graph, we propose the switching function circuit algorithm, also we propose the code assignment algorithm for nodes which is satisfied the directional graph characteristics with designed circuits. We can implement more optimal switching function compare with former algorithm, also we can design the switching function circuit which have any natural number path through the proposed switching function circuit implementation algorithms. Also the proposed switching function implementation using graph theory over finite fields have decrement number of input-output, circuit construction simplification, increment arithmetic speed and decrement cost etc.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.117-123
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• 2013

Let G be a finite non-abelian group. We define the non-commuting graph ${\nabla}(G)$ of G as follows: the vertex set of ${\nabla}(G)$ is G-Z(G) and two vertices x and y are adjacent if and only if $xy{\neq}yx$. In this paper we prove that if G is a finite group with $${\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})$$, then $$G{\simeq_-}\mathbb{A}_{22}$$where $\mathbb{A}_{22}$ is the alternating group of degree 22.