• 충청수학회지
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• 제18권1호
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• pp.73-80
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• 2005

The aim of the paper is to study the connectivity and the edge-connectivity of inserted graph I(G) of a graph G with the help of connectivity and the edge-connectivity of that graph G.

• 대한수학회논문집
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• 제30권2호
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• pp.65-72
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• 2015

The minimum rank mr(G) of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose (i, j)-th entry (for $i{\neq}j$) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The corona $C_n{\circ}K_t$ is obtained by joining all the vertices of the complete graph $K_t$ to each n vertex of the cycle $C_n$. For any t, we obtain an upper bound of zero forcing number of $L(C_n{\circ}K_t)$, the line graph of $C_n{\circ}K_t$, and get some bounds of $mr(L(C_n{\circ}K_t))$. Specially for t = 1, 2, we have calculated $mr(L(C_n{\circ}K_t))$ by the cut-vertex reduction method.

• 대한수학회논문집
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• 제35권4호
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• pp.1045-1056
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• 2020

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, $^{\bar{\mathbb{AG}}}$(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n, m ∈ ℕ such that IⁿJ^m = (0) with Iⁿ, J^m ≠ (0). First, we differentiate when 𝔸𝔾(R) and $^{\bar{\mathbb{AG}}}$(R) coincide. Then, we have characterized the diameter and the girth of $^{\bar{\mathbb{AG}}}$(R) when R is a finite direct products of rings. Moreover, we show that $^{\bar{\mathbb{AG}}}$(R) contains a cycle, if $^{\bar{\mathbb{AG}}}$(R) ≠ 𝔸𝔾(R).

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.261-271
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• 2007

The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• 한국정보처리학회논문지
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• 제4권5호
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• pp.1327-1336
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• 1997

I/O FSM 모델로 표현된 프로토콜들로부터의 시험 계열 생성은 I/OFSM 명세 자체가 강하게 접속되어야 하며 (strongly connected) 상태(state) 수가 최소(minimal)하여야 하며, 그리고 또 결정형(determinstic) 이어야 한다는 가정에서 출발한다. 본 논문에서는 프로토콜을 나타내는 명세 I/OFSM(또는 Graph)이 이러한 가정으로 출발 되는 이유를 객관화 시키고, 또 그래프 재표기 시스템(Graph Rewriting System)을 정의하고, 이를 명세 그래프(명세 I/OFSM)에 적용시켜 기존의 알고리즘보다 훨씬 빨리 강한 접속 여부를 판단하는 알고리즘을 제시한다.

• 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 $leg(G)=b$.

• 대한수학회논문집
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• 제24권2호
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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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• 제23권1_2호
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• pp.257-268
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• 2007

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.

• 전기의세계
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• 제17권2호
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• pp.11-15
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• 1968

One of the most important methods used in the modern analysis of linear networks and systems is the signal flow graph technique, first introduced by S.J. Mason in 1953. In essence, the signal-flow graph technique is a graphical method of solving a set of simultaneous. It can, therefore, be regarded as an alternative to the substitution method or the conventional matrix method. Since a flow-graph is the pictorial representation of a set of equations, it has an obvious advantage, i.e., it describes the flow of signals from one point of a system to another. Thus it provides cause-and-effect relationship between signals. And it often significantly reduces the work involved, and also yields an easy, systematic manipulation of variables of interest. Mason's formula is very powerful, but it is applicable only when the desired quantity is the transmission gain between the source node and sink node. In this paper, author summarizes the signal-flow graph technique, and stipulates three rules for conversion of an arbitrary nonsource node into a source node. Then heuses the conversion rules to obtain various quantities, i.e., networks gains, functions and parameters, through simple graphical manipulations.

• 대한전자공학회논문지
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• 제21권2호
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• pp.19-23
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• 1984

새로운 방향성 적선도(directed product graph; DPG)를 제안하고 적선도에 가지의 방향성과 그 환로의 개념을 도입하므로 상위수학적으로 능동과 또한 결합성 소자까지 포함하는 회로에 대한 Mason공식의 분모(△)항을 그 부호와 소거항에 무관하게 보다 쉽게 구하게 하였다. 또한 이때 회로망 선도에서 나무(tree)를 선택하는데 따르는 제약조건을 제거하였다.