• Korean Journal of Mathematics
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• v.26 no.4
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• pp.741-746
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• 2018

We study the Ihara zeta function of the dumbbell graph $D_{1,1,n}$ of type (1, 1, n) and $D_{1,2,n}$ of type (1, 2, n). Explicit formulas of the zeta functions of the graphs, their radius of convergence, and the connection with the number of closed cycles are given.

• Journal of KIISE:Software and Applications
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• v.34 no.1
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• pp.52-58
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• 2007

In this paper we propose a new robust method to extract accurate human silhouettes indoors with active stereo camera. A prime application is for gesture recognition of mobile robots. The segmentation of distant moving objects includes many problems such as low resolution, shadows, poor stereo matching information and instabilities of the object and background color distributions. There are many object segmentation methods based on color or stereo information but they alone are prone to failure. Here efficient color, stereo and image segmentation methods are fused to infer object and background areas of high confidence. Then the inferred areas are incorporated in graph cut to make human silhouette extraction robust and accurate. Some experimental results are presented with image sequences taken using pan-tilt stereo camera. Our proposed algorithms are evaluated with respect to ground truth data and proved to outperform some methods based on either color/stereo or color/contrast alone.

• 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 ${\Delta}(G_k)=k$.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.3
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• pp.93-100
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• 2004

Test scheduling of SoC (System-on-a-chip) is very important because it is one of the prime methods to minimize the testing time under limited power consumption of SoC. In this paper, a heuristic algorithm, in which test resources are selected for groups and arranged based on the size of product of power dissipation and test time together with total power consumption in core-based SoC is proposed. We select test resource groups which has maximum power consumption but does not exceed the constrained power consumption and make the testing time slot of resources in the test resource group to be aligned at the initial position in test space to minimize the idling test time of test resources. The efficiency of proposed algorithm is confirmed by experiment using ITC02 benchmarks.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.12
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• pp.2201-2206
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• 2008

This paper presents a method of constructing the Linear Digital Switching Function(LDSF) over finite fields. The proposed method is as following. First of all, we extract the input/output relationship of linear characteristics for the given digital switching functions, Next, we convert the input/output relationship to Directed Cyclic Graph(DCG) using basic gates adder and coefficient multiplier that are defined by mathematical properties in finite fields. Also, we propose the new factorization method for matrix characteristics equation that represent the relationship of the input/output characteristics. The proposed method have properties of generalization and regularity. Also, the proposed method is possible to any prime number multiplication expression.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.573-581
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• 2018

In this paper we consider all orientation-preserving ${\mathbb{Z}}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (${\Gamma}(v)$, G(v)) in canonical form for some 5-tuple v = (r, s, t, m, n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (${\Gamma}(v)$, G(v)) that are homeomorphic to the quotient spaces $V_g/{\mathbb{Z}}_{p^2}$ of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_{p^2}$-actions on such handlebodies, up to equivalence.

• ETRI Journal
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• v.21 no.2
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• pp.31-39
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• 1999

Given two sorted lists A=(a0, a1, ${\cdots}$,a${\ell}$-1}) and B=(b0, b1, ${\cdots}$, bm-1), we are to merge these two lists into a sorted list C=(c0,c1, ${\cdots}$, cn-1), where n=${\ell}$+m. Since this is a fundamental problem useful to solve many problems such as sorting and graph problems, there have been many efficient parallel algorithms for this problem. But these algorithms cannot be performed efficiently in the postal model since the communication latency ${\lambda}$, which is of prime importance in this model, is not needed to be considered for those algorithms. Hence, in this paper we propose an efficient merge algorithm in this model that runs in $$2{\lambda}{\frac{{\log}n}{{\log}({\lambda}+1)}}+{\lambda}-1$$ time by using a new property of the bitonic sequence which is crucial to our algorithm. We also show that our algorithm is near-optimal by proving that the lower bound of this problem in the postal model is $f_{\lambda}({\frac{n}{2}})$, where $${\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}{\le}f_{\lambda}({\frac{n}{2}}){\le}2{\lambda}+2{\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}}$$.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.12
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• pp.88-93
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• 2016

This paper presents a method of constructing the highly performance switching circuit(HPSC) over finite fields. The proposed method is as following. First of all, we extract the input/output relationship of linear characteristics for the given digital switching functions, Next, we convert the input/output relationship to Directed Cyclic Graph using basic gates adder and coefficient multiplier that are defined by mathematical properties in finite fields. Also, we propose the new factorization method for matrix characteristics equation that represent the relationship of the input/output characteristics. The proposed method have properties of generalization and regularity. Also, the proposed method is possible to any prime number multiplication expression.

• Journal of the Korean Society of Safety
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• v.21 no.5 s.77
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• pp.60-71
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• 2006

In recent years, the most safety studies have been focused on identifying the relationship between safety climate and safe work behavior in accordance with the awareness that prime causes of accidents are organizational, managerial, and human factors rather than pure technical failures across the world. This study focused empirical research aimed at finding out the safety climate factors and examining the relationships of the safety climate and safe work behavior in construction site in Korea, too. A 10 numbers of safety climate factors were adapted from the Mohamed's study(2002) and tested using PLS-GRAPH 3.0 expecting same results as Mohamed' study. And then the relationship between safety climate and safe work behavior was examined. Only two safety climate factors-personal risk appreciation and worker's safety competence-were found and a strong positive relationship between safety climate and safe work behavior was identified in this study. Discussed in details about the results and implications and suggested further studies.