• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.579-585
• /
• 2012

Let D be a finite digraph with the vertex set V(D) and arc set A(D). A two-valued function $f:V(D){\rightarrow}\{-1,\;1\}$ defined on the vertices of a digraph D is called a signed 2-independence function if $f(N^-[v]){\leq}1$ for every $v$ in D. The weight of a signed 2-independence function is $f(V(D))=\sum\limits_{v{\in}V(D)}\;f(v)$. The maximum weight of a signed 2-independence function of D is the signed 2-independence number ${\alpha}_s{^2}(D)$ of D. Recently, Volkmann [3] began to investigate this parameter in digraphs and presented some upper bounds on ${\alpha}_{s}^{2}(D)$ for general digraph D. In this paper, we improve upper bounds on ${\alpha}_s{^2}(D)$ given by Volkmann [3].

• Journal of the Korean Mathematical Society
• /
• v.41 no.5
• /
• pp.895-912
• /
• 2004

A digraph is locally semicomplete if for every vertex $\chi$, the set of in-neighbors as well as the set of out-neighbors of $\chi$ induce semicomplete digraphs. Let D be a k-connected locally semicomplete digraph with k $\geq$ 3 and g denote the length of a longest induced cycle of D. It is shown that if D has at least 7(k-1)g vertices, then D has a factor composed of k cycles; furthermore, if D is semicomplete and with at least 5k ＋ 1 vertices, then D has a factor composed of k cycles and one of the cycles is of length at most 5. Our results generalize those of [3] for tournaments to locally semicomplete digraphs.

• Journal of Institute of Control, Robotics and Systems
• /
• v.9 no.2
• /
• pp.159-167
• /
• 2003

This study suggests the hybrid fault diagnosis method of signed digraph (SDG) and partial least squares (PLS). SDG offers a simple and graphical representation for the causal relationships between process variables. The proposed method is based on SDG to utilize the advantage that the model building needs less information than other methods and can be performed automatically. PLS model is built on local cause-effect relationships of each variable in SDG. In addition to the current values of cause variables, the past values of cause and effect variables are inputted to PLS model to represent the Process armies. The measured value and predicted one by dynamic PLS are compared to diagnose the fault. The diagnosis example of CSTR shows the proposed method improves diagnosis resolution and facilitates diagnosis of masked multiple-fault.

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

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.385-396
• /
• 2008

For a positive integer m and a digraph D, the m-step competition graph $C^m$ (D) of D has he same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that there are directed walks of length m from u to x and from v to x. Cho and Kim [6] introduced notions of competition index and competition period of D for a strongly connected digraph D. In this paper, we extend these notions to a general digraph D. In addition, we study competition indices of tournaments.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.1
• /
• pp.41-56
• /
• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.55-62
• /
• 2013

The base $l(S)$ of a signed digraph S is the maximum 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. A graph can be regarded as a digraph if we consider its edges as two-sided arcs. A signed cyclic graph $\tilde{C_n}$ is a signed digraph obtained from the cycle $C_n$ by giving signs to all arcs. In this paper, we compute the base of a signed cyclic graph $\tilde{C_n}$ when $\tilde{C_n}$ is neither symmetric nor antisymmetric. Combining with previous results, the base of all signed cyclic graphs are obtained.

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.389-394
• /
• 1989

본 연구에서는 화학공정의 자동화와 관련된 실시간 나프타 분해로 이상진단 시스템의 한 부분을 구성하고 있는 지식기반의 구현을 위하여 공정변수 상호간의 관계를 나타낸 signed directed graph(SDG)를 기반으로 이상에서 파급되는 증상들을 순서대로 나타내는 fault-consequence digraph(FCD)를 지식모델로 사용했고, 이를 사고사례를 이용하여 검토해본 결과 초기에 정확한 이상원인 후보를 찾아내므로써 이상진단 전문가 시스템의 지식모델로 적합함을 알 수 있었다.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.22 no.2
• /
• pp.241-249
• /
• 1997

In this paper, a new technique is proposed for generating a minimum-length synchronizable test sequence that can be applied in the distributed test architecture where both external synchtonization and input/output operation costs are taken into consideration. the method defines a set of transformation rules that constructs a duplex digraph from a given finite state machine representation of a protocol specification rules that constructs a duplex digraph from a given finite state machine representation of a protocol specificatio such that a rural chinese postman tour of the duplex digraph can be used to generate a minimum-length synchronizable test sequence using synchronizable distinguishing sequences as the state identification sequence for each state of the given finite state machine. The method provides an elegant solution to the synchronization problem that arises during the application of a predetermined test sequence in some protocol test architectures that utilize remote testers.

• The Journal of the Korea Contents Association
• /
• v.11 no.1
• /
• pp.56-64
• /
• 2011

It is difficult to discover frequent itemsets based on whole data from data stream since data stream has the characteristics of infinity and continuity. Therefore, a specialized data mining method, which reflects the properties of data and the requirement of users, is required. In this paper, we propose the method of FIMWB discovering the frequent itemsets which are reflecting the property that the recent events are more important than old events. Data stream is splitted into batches according to the given time interval. Our method gives a weighted value to each batch. It reflects user's interestedness for recent events. FP-Digraph discovers the frequent itemsets by using the result of FIMWB. Experimental result shows that FIMWB can reduce the generation of useless items and FP-Digraph method shows that it is suitable for real-time environment in comparison to a method based on a tree(FP-Tree).