• ETRI Journal
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• v.31 no.3
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• pp.327-329
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• 2009

In a network, broadcasting is the dissemination of a message from a source node holding a message to all the remaining nodes through a call. This letter proposes a one-to-all broadcasting algorithm in the Petersen-torus network PT(n, n) for the single-link-available and multiple-link-available models. A PT(n, n) is a regular network whose degree is 4 and number of nodes is $10n^2$, where the Petersen graph is set as a basic module, and the basic module is connected in the form of a torus. A broadcasting algorithm is developed using a divide-and-conquer technique, and the time complexity of the proposed algorithm approximates n+4, the diameter of PT(n, n), which is the lower bound of the time complexity of broadcasting.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.307-315
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• 2018

Let G be a simple connected graph with n vertices and m edges, with a sequence of vertex degrees $d_1{\geq}d_2{\geq}{\cdots}{\geq}d_n$ > 0. A vertex-degree topological index, referred to as harmonic index, is defined as $H={\sum{_{i{\sim}j}}{\frac{2}{d_i+d_j}}$, where i ~ j denotes the adjacency of vertices i and j. Lower and upper bounds of the index H are obtained.

• Research in Mathematical Education
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• v.8 no.2
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• pp.81-93
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• 2004

This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• Journal of Internet Computing and Services
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• v.15 no.5
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• pp.95-105
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• 2014

In this paper, we present a novel ant-based hierarchical clustering algorithm, where ants repeatedly hop from one node to another over a weighted directed graph of k-nearest neighborhood obtained from a given dataset. We introduce a notion of node pheromone, which is the summation of amount of pheromone on incoming arcs to a node. The node pheromone can be regarded as a relative density measure in a local region. After a finite number of ants' hopping, we remove nodes with a small amount of node pheromone from the directed graph, and obtain a group of strongly connected components as clusters. We iteratively do this removing process from a low value of threshold to a high value, yielding a hierarchy of clusters. We demonstrate the performance of the proposed algorithm with synthetic and real data sets, comparing with traditional clustering methods. Experimental results show the superiority of the proposed method to the traditional methods.

• Journal of the Korean Solar Energy Society
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• v.29 no.2
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• pp.1-7
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• 2009

Use of the PV(photovoltaic) generation system is increased in such areas as remote mountain places or islands at which electrical energy is not serviced. The stand alone PV system is required the power storage products such as battery, fly wheel and super capacitor. Several lead storage batteries are connected in series to get high voltages. The life of lead storage battery is shortened when over charge or over discharge takes place. So, it is needed to control batteries not to be overcharged or be discharged deeply. Voltage of each battery was ignored in former control methods in which overall voltage was used to control charge or discharge battery. In this study, the charging and discharging voltage variations of sealed lead storage batteries with l2V/l.2A were investigated step by step experiments. The results of the test show that one should consider and specify the state of each battery to prevent overcharge or deep discharge. With the basis of the experiments, we designed a monitoring unit to monitor battery voltages simultaneously using micro-controller. The unit measures voltage of 20 batteries simultaneously and displays data on the color LCD monitor with curved line graph. It also sends data to PC using the RS232C communication port. The designed unit was adapted to stand alone PV system with 1kW capacity and lead storage batteries are connected to the PV generation system. The number of lead storage batteries was 10 in series and 12V/250Ah each. Resistive load with 3kW was used for discharging.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.2
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• pp.335-341
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• 2017

This paper proposes an image-processing algorithm for inspecting double-cut defects in the motor shaft manufacturing process. The algorithm consists of extracting the outline using the brightness of the image, obtaining a binarized boundary graph using the extracted outline, and determining the defects from the graph. Defects in which two cut surfaces are separated are considered type 1 defects, and those in which two cut surfaces are connected are defined as type 2 defects. In an actual manufacturing process, 112 good samples and 44 defective samples (34 type 1 defects and 10 type 2 defects) were collected and used to verify the algorithm. The samples were judged with 100% accuracy for both type 1 and type 2 defects. The algorithm will be used in the field after securing reliability for various samples.

• Journal of the Korea Society of Computer and Information
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• v.18 no.5
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• pp.95-102
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• 2013

In metabolomics, metabolic pathway is represented by well-displayed graph. Metabolic pathways, especially, have a complex binding structure, which makes the graphical representation hard to visualize. There is a problem that edge crossings exponentially increase as the number of nodes grows. To apply automatic graph layout techniques to the genome-scale metabolic flow of metabolism domains, it is very important to reduce unnecessary edge crossing on a metabolic pathway layout. we proposed a metabolic pathway layout algorithm based on 2-layer layout. Our algorithm searches any meaningful component existing in a pathway, such as circular components, highly connected nodes, and the components are drawn in upper layer. Then the remaining subgraphs except meaningful components are drawn in lower layer by utilizing a new radial layout algorithm. It reduces ultimately reduced the number of edge crossings. This algorithm is the basis of flexible analysis for metabolic pathways.

• Journal of the Korea Society of Computer and Information
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• v.18 no.6
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• pp.71-79
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• 2013

Metabolic pathway, represented by well-displayed graph, have a complex binding structure, which makes the graphical representation hard to visualize. To apply automatic graph layout techniques to the genome-scale metabolic flow of metabolism domains, it is very important to reduce unnecessary edge crossing on a metabolic pathway layout. we proposed a metabolic pathway layout algorithm based on 3-layer layout. Our algorithm searches any meaningful component existing in a pathway, such as circular components, highly connected nodes, and the components are drawn in middle layer. Then the remaining subgraphs except meaningful components are drawn in upper and lower layer by utilizing a new radial layout algorithm. It reduces ultimately reduced the number of edge crossings. Our algorithm solve the problem that edge crossings exponentially increase as the number of nodes grows.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1397-1404
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• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.