• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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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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• v.24 no.1_2
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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 $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• The Transactions of the Korea Information Processing Society
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• v.4 no.5
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• pp.1327-1336
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• 1997

Test generation from the communication protocol specified in I/OFSM protocol is based on the asumption that the specification S and implemenataiton I are storngly, connected,minmal and deterministic.In this paper,we identify why these asumptions are necessary for minimal test cases genration from I/OFSM protocol speci-fication,and we propose a graph Rewriting System and its application to the specification I/OFSM for verifying its storng cinnectivity.We prove that the suggested algorithm is more dffcient thah the traditional strongly connected compoment find algorithm.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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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 $leg(G)=b$.

• 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.23 no.1_2
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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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• v.17 no.2
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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.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.19-23
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• 1984

A new directed product graph(DPG) is proposed from the product graph for electrical networks. By introducing the direction of an dege and the concept of a loop to product graph, it is more easy and rapid to obtain topologically the denominator of Mason's formula without relation of the sign rule and without arising terms cancelled. Also the constraints of tree selection at a given network-graph can be removed.