• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.313-323
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• 2007

The equitable total chromatic number ${\chi}_{et}(G)$ of a graph G is the smallest integer ${\kappa}$ for which G has a total ${\kappa}$-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determine the equitable total chromatic number of one class of the graphs.

• Journal of the Optical Society of Korea
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• v.16 no.3
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• pp.215-220
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• 2012

In an earlier work, we proposed the chromatic dispersion monitoring technique of non-return to zero (NRZ) signal based on clock-frequency component (CFC) through numerical simulations. However, we have not yet shown any experimental demonstration or analytic derivation of it. In this paper, we show an experimental demonstration and analytic derivation of the proposed chromatic dispersion monitoring technique. We confirm that the experimental results and the analytic results correspond with the simulation results. We also demonstrate that monitoring range and accuracy can be improved by using a simple clock-extraction method.

• International Journal of Computer Science & Network Security
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• v.21 no.9
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• pp.79-85
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• 2021

The locating-chromatic number denote by 𝛘_𝐿(G), is the smallest t such that G has a locating t-coloring. In this research, we determined locating-chromatic number for subdivision of certain barbell operation of origami graphs.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.525-534
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• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• The Journal of the Korea Contents Association
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• v.10 no.7
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• pp.107-114
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• 2010

Color is a sense signal for human to perceive being through light, and the color is divided into chromatic color and achromatic color. Chromatic color has hue, intensity, and saturation, but achromatic color has only intensity among the properties of chromatic color and doesn't have hue and saturation. Therefore it is important to split colors of image into area for human to perceive colors and not to perceive ones based on vision of human being. In this paper, we find a function to split colors of image into chromatic region of chromatic color region and achromatic region of achromatic color region. First, the input image of RGB color space is converted into the image of HSI color space in consideration of human vision and get a binary image from the converted image. After then, a function to split colors into ROC(ROC: Region of chromatic.) and ROA(ROA:Region of achromatic) is yield. It is difficult to split color of a general image into ROC and ROA. Therefore, to get the chromatic area and achromatic area, we make gradient images to have all range of intensity and range of saturation and to have a little range of hue and yield the function. The evaluation is tested using subjective-quality by 50 non-experts for result images of test images and general images. The results of the proposed method get better 27.5~32.96% than these of the conventional method

• Journal of the Korea Society of Computer and Information
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• v.19 no.5
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• pp.19-25
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• 2014

In this paper, I seek the chromatic number, the maximum number of colors necessary when adjoining vertices in the plane separated apart at the distance of 1 shall receive distinct colors. The upper limit of the chromatic number has been widely accepted as $4{\leq}{\chi}(G){\leq}7$ to which Hadwiger-Nelson proposed ${\chi}(G){\leq}7$ and Soifer ${\chi}(G){\leq}9$ I firstly propose an algorithm that obtains the minimum necessary chromatic number and show that ${\chi}(G)=3$ is attainable by determining the chromatic number for Hadwiger-Nelson's hexagonal graph. The proposed algorithm obtains a chromatic number of ${\chi}(G)=4$ assuming a Hadwiger-Nelson's hexagonal graph of 12 adjoining vertices, and again ${\chi}(G)=4$ for Soifer's square graph of 8 adjoining vertices. assert. Based on the results as such that this algorithm suggests the maximum chromatic number of a planar graph is ${\chi}(G)=4$ using simple assigned rule of polynomial time complexity to color for a vertex with minimum degree.

• Journal of Fashion Business
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• v.12 no.5
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• pp.94-110
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• 2008

The main objective of this research was to understand the characteristics of separation color coordination of contemporary female fashion through the analysis of 'pre-a-porter Collections' of four collections (i. e. cities) - Paris, Milan, New York, London - from the periods of 2004 S/S to 2008/9 A/W. The data collection of 265 was done by reviewing 'pre-a-porter Collections' magazine and total 265 observations were made. Statistical analysis of frequency and also qualitative interpretation of separation color coordination characteristics were completed. The main findings were; (1) In separation color coordination of contemporary women's fashion collections, there were three main types of color scheme which were classified into seven detailed categories of color combination. First was the achromatic color & one chromatic separation color scheme which was classified into four categories of - black & white, black & grey, white & grey, and grey & grey - color combination. Second was the chromatic colors & one achromatic separation color scheme which classified into two categories of achromatic & chromatic color & one achromatic separation color combination, and chromatic colors & one achromatic separation color combination. Third was chromatic colors and one chromatic separation color combination. (2) The achromatic colors and one chromatic separation color scheme showed two phases of reinforcing the strong and modern image, or softening the hard and dull image of achromatic color combination. In color schemes which used more than two chromatic colors, the separation color frequently converted the tedious and monotonous fashion image, which caused by identical or similarity in color or tone harmony, into more attractive and interesting. (3) In conclusion, through the various use and coordination of various color schemes, color harmony and separation colors, the separation color coordination in contemporary female fashion has been suggested the effective way of color combination which can lead the visual pleasure and the vitality along with the unity and the harmony. This characteristics can create various images and visual diversity for fashion. The types and the use of color scheme and separation color showed different trends in four collections.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.391-399
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• 2019

Let R be a commutative ring with identity and let M be an R-module. The main purpose of this paper is to calculate the chromatic number of the zero-divisor graphs over modules.

• Tribology and Lubricants
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• v.24 no.1
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• pp.7-13
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• 2008

In this work, a simple and low cost sensor technique is proposed to test oil color in real time using in-line sensor. It is presented to use a ratio of intensity in red wavelength range to intensities of green and blue wavelength ranges (defined as a 'chromatic ratio') in order to estimate the oil color change. The proposed sensor technique is realized by irradiating a white LED as light source and a RGB color sensor as photoreceiver, and the chromatic ratio of various types of used oils are measured. The results show that chromatic ratio generally reflects chemical deterioration of oil, including oil oxidation and thermal degradation. It is concluded that the proposed sensor could be used for an effective oil monitoring technology.

• Journal of the Optical Society of Korea
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• v.16 no.4
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• pp.336-342
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• 2012

A low-cost optimal double-prism method is proposed by using the developed MATLAB program to correct chromatic aberration. We present an efficient approach to choose a couple of low-cost glasses to obtain a low aberration double prism. The doublet prisms were made of two lead-free glasses. The relative partial dispersion of the two lead-free glasses is identical and their Abbe numbers are different greatly. The proposed design aims to minimize chromatic aberration, such as in apochromats, for paraxial ray tracing. Finally, an optimization design for real ray tracing can be evaluated by the chromatic aberration curve with a minimal area.