• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.843-853
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• 1998

We establish bounds for the domination number of a digraph in terms of the minimum indegree and the order, and then we find a sharp upper bound for the domination number of a weak digraph with minimum indegree one. We also determine the domination number of a random digraph.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.637-646
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• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1405-1410
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• 2009

A tripartite $\gamma$-digraph is an orientation of a tripartite multigraph that is without loops and contains at most $\gamma$ edges between any pair of vertices from distinct parts. In this paper, we obtain necessary and sufficient conditions for sequences of non-negative integers in non-decreasing order to be the sequences of numbers, called marks (or $\gamma$-scores), attached to the vertices of a tripartite $\gamma$-digraph.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.359-366
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• 2014

A three-valued function f defined on the vertices of a digraph D = (V, A), $f:V{\rightarrow}\{-1,0,+1\}$ is a minus total dominating function(MTDF) if $f(N^-(v)){\geq}1$ for each vertex $v{\in}V$. The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.627-641
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• 2008

A two-colored digraph D is primitive if there exist nonnegative integers hand k with h + k > 0 such that for each pair (i, j) of vertices there exists an (h, k)-walk in D from i to j. The exponent of the primitive two-colored digraph D is the minimum value of h + k taken over all such hand k. In this paper, we give the tight upper bound on the exponents of a class of primitive two-colored digraphs with (s + 1) n-cycles and one (n - 1)-cycle, and the characterizations of the extremal two-colored digraphs.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.395-402
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• 2012

A digraph D is primitive if there is a positive integer $k$ such that there is a walk of length $k$ between arbitrary two vertices of D. The exponent of a primitive digraph is the least such $k$. Wielandt graph $W_n$ of order $n$ is known as the digraph whose exponent is $n^2-2n+2$, which is the maximum of all the exponents of the primitive digraphs of order n. It is known that the diameter of the multiple direct product of a digraph $W_n$ strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of $W_n$. In this paper, we find the diameter of the direct product of Wielandt graphs.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.29-36
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• 2015

A signed digraph S is the digraph D by assigning signs 1 or -1 to each arc of D. The base of S is the minimum number k such that there is a pair walks which have the same initial and terminal point with length k, but different signs. In this paper we show that for $n{\geq}5$ the upper bound of the base of a primitive non-powerful signed tournament Sn, which is the signed digraph by assigning 1 or -1 to each arc of a primitive tournament $T_n$, is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.393-393
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• 2000

FTA(Fault Tree Analysis) is a safety analysis method that focuses on one particular accident or main system failure and provides a method of determining causes of that event. While most of the statistical and cut set analysis have been automated, actual construction of the fault-tree is usually done manually. Manual construction of the fault-tree is extremely time consuming and it requires high level of expertise and experience. In addition to the time involved, different analyst often produces different fault-trees either by incorrect logic or omission of certain events. Automatic fault-tree construction system can be efficient in solving above problems. This study presents a new Digraph-FT conversion algorithm that leads automatic FTA system.

• East Asian mathematical journal
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• v.30 no.3
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• pp.355-360
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• 2014

Let D be a finite digraph with the vertex set V (D) and the arc set A(D). A function f : $V(D){\rightarrow}\{-1,\;1\}$ defined on the vertices of a digraph D is called a bad function if $f(N^-(v)){\leq}1$ for every v in D. The weight of a bad function is $f(V(D))=\sum\limits_{v{\in}V(D)}f(v)$. The maximum weight of a bad function of D is the the negative decision number ${\beta}_D(D)$ of D. Wang [4] studied several sharp upper bounds of this number for an undirected graph. In this paper, we study sharp upper bounds of the negative decision number ${\beta}_D(D)$ of for a digraph D.

• 한국가스학회:학술대회논문집
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• 1997.09a
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• pp.133-137
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• 1997