• 한국정보통신학회논문지
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• 제17권9호
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• pp.2091-2096
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• 2013

본 논문에서는 방향성 그래프에 기초하여 절점들 간의 입출력 관계가 트리의 특성을 갖는 연관관계를 분할연산기법과 수학적 해석을 통하여 함수로 변환하고 이를 회로 설계하는 방법에 대하여 논의하였다. 기존에 제안된 알고리즘이 임의의 절점수를 갖는 방향성 그래프에 대하여 같은 수의 잉여절점수를 삽입함으로써 생성되는 매개변수들이 양의 정수로 표현되지 못하여 회로의 설계가 불가능하게 되는 문제점이 있었다. 이를 개선하기 위해서 본 논문에서는 트리의 성질을 수학적으로 해석하여 주어진 임의의 절점수를 가지는 방향성 그래프에 대하여 절점들의 관계를 규명해주는 매개변수들과 논리레벨 P의 승수로 표현되어 항상 양의 정수 값을 갖도록 레벨 간에 각기 다른 잉여절점을 삽입하여 효율적인 회로설계를 하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권8호
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• pp.2178-2198
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• 2024

Graph-based document models have good capabilities to reveal inter-dependencies among unstructured text data. Natural language processing (NLP) systems that use such models as an intermediate representation have shown good performance. This paper proposes a novel fuzzy graph-based document model and to demonstrate its effectiveness by applying fuzzy logic tools for text summarization. The proposed system accepts a text document as input and identifies some of its sentence level features, namely sentence position, sentence length, numerical data, thematic word, proper noun, title feature, upper case feature, and sentence similarity. The fuzzy membership value of each feature is computed from the sentences. We also propose a novel algorithm to construct the fuzzy graph as an intermediate representation of the input document. The Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metric is used to evaluate the model. The evaluation based on different quality metrics was also performed to verify the effectiveness of the model. The ANOVA test confirms the hypothesis that the proposed model improves the summarizer performance by 10% when compared with the state-of-the-art summarizers employing alternate intermediate representations for the input text.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.511-524
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• 2023

An L(p₁, p₂, p₃, . . . , p_m)-labeling of a graph G is an assignment of non-negative integers, called as labels, to the vertices such that the vertices at distance i should have at least pi as their label difference. If p₁ = 4, p₂ = 3, p₃ = 2, p₄ = 1, then it is called a L(4, 3, 2, 1)-labeling which is widely studied in the literature. A L(4, 3, 2, 1)-path coloring of graphs, is a labeling g : V (G) → Z⁺ such that there exists at least one path P between every pair of vertices in which the labeling restricted to this path is a L(4, 3, 2, 1)-labeling. This concept was defined and results for some simple graphs were obtained by the same authors in an earlier article. In this article, we study the concept of L(4, 3, 2, 1)-path coloring for complete bipartite graphs, 2-edge connected split graph, Cartesian product and join of two graphs and prove an existence theorem for the same.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• 대한수학회보
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• 제50권6호
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• pp.2021-2026
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• 2013

Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

• 대한수학회보
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• 제56권6호
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• pp.1485-1495
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• 2019

The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional $Pr{\ddot{u}}fer$ domains. We prove that ${\mid}SStar(R){\mid}={\mid}Star(R){\mid}+{\mid}Spec(R){\mid}+ {\mid}Idem(R){\mid}$ where Idem(R) is the set of all nonzero idempotent prime ideals of R if and only if R is a $Pr{\ddot{u}}fer$ domain with Y -graph spectrum, that is, R is a $Pr{\ddot{u}}fer$ domain with exactly two maximal ideals M and N and $Spec(R)=\{(0){\varsubsetneq}P_1{\varsubsetneq}{\cdots}{\varsubsetneq}P_{n-1}{\varsubsetneq}M,N{\mid}P_{n-1}{\varsubsetneq}N\}$. We also characterize non-local $Pr{\ddot{u}}fer$ domains R such that ${\mid}SStar(R){\mid}=7$, respectively ${\mid}SStar(R){\mid}=14$.

• 대한수학회지
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• 제56권4호
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• 대한수학회보
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• 제59권3호
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.

• 대한수학회지
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• 제32권1호
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• pp.1-5
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• 1995

• 전기의세계
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• 제22권5호
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• pp.12-18
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• 1973

This paper deals with Linear Programming by Signal Flow Graph technique which is different from that of Mason and Coates. The objective function is regarded as variable, and slack variable node, artificial variable node and objective function variable (constant) node are newly defined, which shows the process for optimization of solution very intuitively. Also methods for solving L.P. and examples with subject to Ax.leq.b, Ax=b and Ax.geq.b are presented.