• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.39-48
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• 2006

Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.37-47
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• 2006

In this paper we characterize the graphs whose inserted graphs are Hamiltonian, and we study the relationship between Hamiltonian graphs and inserted graphs. Also we prove that if a connected graph G contains at least 3 vertices then inserted graph of the square of G is Hamiltonian and if G contains at least 3 edges then the square of inserted graph of G is Hamiltonian.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.151-159
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• 2013

An $L(j,k)$-labeling of a graph G is a vertex labeling such that the difference of the labels of any adjacent vertices is at least $j$ and that of any vertices of distance two is at least $k$ for given $j$ and $k$. The minimum span of all L(2, 1)-labelings of G is called the ${\lambda}$-number of G and is denoted by ${\lambda}(G)$. In this paper, we find a lower bound of the ${\lambda}$-number of the Cartesian product $K_m{\Box}C_n$ of the complete graph $K_m$ of order $m$ and the cycle $C_n$ of order $n$. In fact, we show that when $n{\geq}3$, ${\lambda}(K_4{\Box}C_n){\geq}7$ and the equality holds if and only if n is a multiple of 8. Moreover when $m{\geq}5$, ${\lambda}(K_m{\Box}C_n){\geq}2m-1$ and the equality holds if and only if $n$ is even.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.43-47
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• 1997

A procedure presented in this paper generates test sequences to check the conformity of an implementation with a protocol specification, which is modeled as a deterministic finite state machine (FSM). Given a FSM, a common procedure of test sequence generation, first, constructs a directed graph which edges include the state check after each transition, and produces a symmetric graph G* from and, finally, finds a Euler tour of G*. We propose a technique to determine a minimum-cost tour of the transition graph of the FSM. The proposed technique using Multiple Unique State Signature (MUSS) solves an open issue that one MUIO sequence assignment may lead to two more edges of unit cost being replicated to from G* while an optimal assignment may lead to the replication of a single edge of high cost. In this paper, randomly generated FSMs have been studied as test cases. The result shows that the proposed technique saves the cost 4∼28% and 2∼21% over the previous approach using MUIO and MUSP, respectively.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.2
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• pp.429-434
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• 2017

In a graph G=(V, E) with n vertices, there is an unique box which is finally laid on each vertex. Thus each vertex and box is both numbered from 1 to n and the box i should be laid on the vertex i. But, the box ${\pi}$(i) is initially located on the vertex i according to a permutation ${\pi}$. In each step, the robot can walk along an edge of G and can carry at most one box at a time. Also when arriving at a vertex, the robot can swap the box placed there with the box it is carrying. The problem is to minimize the total step so that every vertex has its own box, that is, the shuffled boxes are sorted. In this paper, we shall find an upper bound of the minimum number of steps and show that the movement of the robot is found in $O(n^2)$ time when G is a cycle.

• Proceedings of the Korea Information Processing Society Conference
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• 2020.05a
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• pp.595-598
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• 2020

IoU (Intersection over Union) is the most commonly used index in target detection. The core requirement of target detection is what is in the image and where. Based on these two problems, classification training and positional regression training are needed. However, in the process of position regression, the most commonly used method is to obtain the IoU of the predicted bounding box and ground-truth bounding box. Calculating bounding box regression losses should take into account three important geometric measures, namely the overlap area, the distance, and the aspect ratio. Although GIoU (Generalized Intersection over Union) improves the calculation function of image overlap degree, it still can't represent the distance and aspect ratio of the graph well. As a result of technological progress, Bounding-Box is no longer represented by coordinates x,y,w and h of four positions. Therefore, the IoU can be further optimized with the center point and aspect ratio of Bounding-Box.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.11a
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• pp.221-226
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• 2006

We usually use two techniques(influence function and local influence) for detecting outliers. But, we cannot use these difficult techniques in elementary industrial statistics course for college students. We can use some simple graphical methods(box plot, dandelion seed plot, influence graph and cumulative deletion plot) for univariate and bivariate outlier detection and outlier effect in elementary industrial statistics course for college students.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.60.5-60
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• 2001

It is very difficult to design and analyze the relay circuit because one have to consider and analyze in order the behavior in which the relay contacts. In this paper, we propose the relay circuit to EMPG (Extended Mark Flow Graph) convension with a box´s characteristic equation. It will give you a lot of benefits in case of analysis and check of the relay circuit to convert the relay circuit into EMPG.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.692-695
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• 2001

The EMFG(Extended Mark Flow Graph) is not only a powerful tool to. designing the discrete-event system conceptually or specifically but also a good representation tool for implementing the system directly. We present a transitions-firing process and automatic changes of the number of marks in each box as a firing determination algorithm with the incident matrix and the state transition equation. The convenient analysis and design of a system as well as Computer Aided Design is possible because the operations of an EMFG ran be represented in the mathematical analysis with ease.