• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.1-6
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• 2014

Let G = (V ; E) be a simple undirected graph without loops and multiple edges, the vertex and edge sets of it are represented by V = V (G) and E = E(G), respectively. A weighting w of the edges of a graph G induces a coloring of the vertices of G where the color of vertex v, denoted $S_v:={\Sigma}_{e{\ni}v}\;w(e)$. A k-edge-weighting of a graph G is an assignment of an integer weight, w(e) ${\in}${1,2,...,k} to each edge e, such that two vertex-color $S_v$, $S_u$ be distinct for every edge uv. In this paper we determine an exact 3-edge-weighting of complete graphs $k_{3q+1}\;{\forall}_q\;{\in}\;{\mathbb{N}}$. Several open questions are also included.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.573-581
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• 2018

In this paper we consider all orientation-preserving ${\mathbb{Z}}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (${\Gamma}(v)$, G(v)) in canonical form for some 5-tuple v = (r, s, t, m, n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (${\Gamma}(v)$, G(v)) that are homeomorphic to the quotient spaces $V_g/{\mathbb{Z}}_{p^2}$ of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_{p^2}$-actions on such handlebodies, up to equivalence.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.1
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• pp.42-49
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• 1987

This paper describes test-pattern generation and it;s sequence for fan out-free Combinational logic network with multiple faults. The method for detecting multiple faults, in systematic way, is established by using characteristic graphs. This method is applied even in the case of fan out-reconvergent combinational logic networks. In this case, the network is decomposed into a set of fan out-free sybnetworks so as to use the characteristic graphs, and minimal test patterns are generated seperately. The each test set is combined and the test pattern for fan out-reconvergent networks are derived. According to corresponding characteristic graph, additional test patterns to detect multiple faults are simply derived.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.11
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• pp.1353-1362
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• 1999

그래프 드로잉이란 추상적인 그래프를 시각적으로 구성하여 2차원 평면상에 그려주는 작업으로 대칭성은 그래프 드로잉시 고려해야 하는 미적 기준들 중에서 그래프의 구조 및 특성을 표현해주는 가장 중요한 기준이다. 그러나 일반 그래프에서 대칭성을 찾아 그려 주는 문제는 NP-hard로 증명이 되어 있기 때문에 현재까지는 트리, 외부평면 그래프, 직병렬 유향 그래프나 평면 그래프 등으로 대상을 한정시켜 연구가 진행되어 왔다. 본 논문에서는 병렬 컴퓨터나 컴퓨터 네트워크 구조를 가시화 시키기 위하여 많이 사용되는 그래프인 상호연결망(interconnection network)의 대칭성을 분석하고 분석된 대칭성을 최대로 보여주는 대칭 드로잉 알고리즘을 제안하였다. 그리고 이를 기반으로 하여 상호연결망의 기존 드로잉 방법들과 본 논문에서 제안한 대칭 드로잉 등 다양한 드로잉을 지원하는 WWW 기반의 상호연결망 드로잉 시스템을 구현하였다.Abstract Graph drawing is constructing a visually-informative drawing of an abstract graph. Symmetry is one of the most important aesthetic criteria that clearly reveals the structures and the properties of graphs. However, the problem of finding geometric symmetry in general graphs is NP-hard. So the previous work has focused on the subclasses of general graphs such as trees, outerplanar graphs, series-parallel digraphs and planar graphs.In this paper, we analyze the geometric symmetry on the various interconnection networks which have many applications in the design of computer networks, parallel computer architectures and other fields of computer science. Based on these analysis, we develope algorithms for constructing the drawings of interconnection networks which show the maximal symmetries.We also design and implement Interconnection Network Drawing System (INDS) on WWW which supports the various drawings including the conventional drawings and our suggested symmetric drawings.

• Journal of the Korean Institute of Landscape Architecture
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• v.25 no.2
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• pp.73-81
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• 1997

The main purpose of this study was to develop a new method for evaluation of stream naturalness in order to appraise and prescribe for streams effectively in the process of ecological restoration of stream corridors. The results are as follows : 1) For this purpose six factors were selected on considering the spatial axes of stream corridor variation and total 20 descriptors about the physical structure were selected. 2) The calculation of S.N.I. for each segment was consisted of three steps, such as calculation of S.N.I.s of the individual descriptors, averaging all the descriptors's for each factor, and finally averaging the factors's for the Total S.N.I. 3) The evaluation unit was decided to be 100m size. The score system ranging 1~5 was adopted. Weighting parameters of factors were unified with each other. 4) A GIS model was adopted for classification, calculation, querying, analysing, and presenting S.N.I. information. And the format of S.N.I. maps including statistical graphs and other spatial watershed information was designed for the GIS odel. The naturalness of stream corridor was was investigated by the naturalness of habitat, and assessed by the descriptors focused on physical structure, therefore the S.N.I. can manifest prescriptions for restoration of the stream corridor. On the other hand because some evaluation factors such as water quality, water volume, fauna, flora, functions of stream exosystem has been excluded, S.N.I. could have some limits on representing the full aspects of stream naturalness. This evaluation method is hypothetical one, so it would be investigated through iterative applicatons.

• Journal of the Korea Society of Computer and Information
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• v.20 no.1
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• pp.227-235
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• 2015

In this paper, I propose a linear time algorithm devised to produce exact solution to NP-complete maximum clique problem. The proposed algorithm firstly, from a given graph G=(V,E), sets vertex $v_i$ of the maximum degree ${\Delta}(G)$ as clique's major vertex. It then selects vertex $v_j$ of ${\Delta}(G)$ among vertices $N_G(v_i)$ that are adjacent to $v_i$, only to determine $N_G(v_i){\cap}N_G(v_j)$ as candidate cliques w and $v_k$. Next it obtains $w=w{\cap}N_G(v_k)$ by sorting $d_G(v_k)$ in the descending order. Lastly, the algorithm executes the same procedure on $G{\backslash}w$ graph to compare newly attained cliques to previously attained cliques so as to choose the lower. With this simple method, multiple independent cliques would also be attainable. When applied to various regular and irregular graphs, the algorithm proposed in this paper has obtained exact solutions to all the given graphs linear time O(n).

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.491-500
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• 2014

The base of a signed digraph S is the minimum number k such that for any vertices u, v of S, there is a pair of walks of length k from u to v with different signs. Let K be a signed complete graph of order n, which is a signed digraph obtained by assigning +1 or -1 to each arc of the n-th order complete graph $K_n$ considered as a digraph. In this paper we show that for $n{\geq}3$ the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.161-169
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• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.155-163
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• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.967-983
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• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.