• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.45-64
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• 2015

In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak [15] first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus 3. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We prove that these graphs satisfy the conjecture.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.139-151
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• 2016

A k-total-coloring of a graph G is a coloring of $V{\cup}E$ using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ of G is the smallest integer k such that G has a k-total-coloring. Let G be a planar graph with maximum degree ${\Delta}$. In this paper, it's proved that if ${\Delta}{\geq}7$ and G does not contain adjacent 5-cycles, then the total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ is ${\Delta}+1$.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.353-366
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• 2024

A total coloring of a graph G is an assignment of colors to both the vertices and edges of G, such that no two adjacent or incident vertices and edges of G are assigned the same colors. In this paper, we have discussed the total coloring of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n) and also obtained the total chromatic number of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n).

• Journal of Technologic Dentistry
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• v.36 no.4
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• pp.247-253
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• 2014

Purpose: The aim of this study was to evaluate the effect of colored zirconia with different coloring liquids. Methods: Total 30 specimens were prepared. Specimens were classified into 6 groups: IPS e.max Ceram(P), Uncolored zirconia(C), VITA In-Ceram$^{(R)}$2000 YZ LL1(L), Zirkonzahn coloring liquid(Z), Wieland coloring liquid(W), and Kuwotech coloring liquid(K). Four different types of zirconia coloring liquid, VITA In-Ceram$^{(R)}$ 2000 YZ LL1(VITA Zahnfabrik, Germany), Zirkonzahn coloring liquid(Zirkonzahn, Italy), Wieland coloring liquid(Wieland, Germany), Kuwotech coloring liquid(Kuwotech, Korea) were used to fabricate colored zirconia by using infiltrating method and then completely sintered. The color of the all specimens was measured using the spectrophotometer(CM-2600d, Konica Minolta, Japan) and expressed in terms of the 3-coordinated values(CIE $L^*a^*b^*$). Color differences were calculated using the equation $${\Delta}E^*=[({\Delta}L^*)^2+({\Delta}a^*)^2+({\Delta}b^*)^2]^{1/2}$$. Results: $L^*a^*b^*$ values of the colored zirconia were affected by the coloring liquids. The uncolored zirconia(C) group showed the highest $L^*$ value and zirkonzahn coloring liquid(Z) group showed the lowest $L^*$ value. Zirkonzahn coloring liquid(Z) showed the highest $a^*$ value and VITA In-Ceram 2000 YZ LL1(L) group showed the highest $b^*$ value. Generally, the color difference(${\Delta}E^*$) in all groups showed higher than 3.7 except between IPS e.max Ceram(P) and wieland coloring liquid(W) group. Conclusion: Within the limitations of this study, various coloring liquids influenced the $L^*$, $a^*$, and $b^*$ values of colored zirconia. IPS e.max Ceram(P) and wieland coloring liquid(W) group did not show clinically perceiving color difference.

• Journal of the Korea Fashion and Costume Design Association
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• v.12 no.2
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• pp.67-73
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• 2010

Whole process of textile printing is made by computer and it remarkably improves environment problem. This digital textile printing is becoming next step environment friendly textile printing method. But, still now range of textile possible for digital textile printing is limited, and also color analysis according to fiber types is not completed. The ink printed on the fabrics through DTP printer can be absorbed and fixed into textile without any blots by pre-treatment using suitable media solution for fabrics types. The chemical formulation of media solution used in the pre-treatment process varies according to the types of textiles and inks for DTP products. First, I studied reference books or articles about color analysis of digital textile printing. Second, I recorded pre-process, printing, post-process and coloring of silk, wool, nylon at same condition. After that, I analyzed $L^*\;a^*\;b^*$, Total K/S, ${\Delta}E$ and studied color intensity and coloring. According to this study, I suggested particular textile special for coloring and manual for affective coloring control. It showed that the performance of the digital printing on the Silk, Wool and Nylon blend fabrics treated by the media solution developed in this study was better than the one treated by the previous media solution for each single inks.

• 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 Fashion Business
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• v.19 no.1
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• pp.77-94
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• 2015

Due to the inflammatory of body exposure it did not become popular to the Korean nation but the body painting as a body art is definitely required for it be become a new pure artwork. In this body painting color is the core factor for visual part and expression and coloring obtained from the color is very important in creating effective image. In Korea beauty industry the researches are limited to the study on coloring expression of general beauty makeup. Therefore, this research analyzes color images in recent body painting artworks by defining characteristics of colors and coloring applied by theme. For the research subjects, dominant and secondary colors were extracted from the artworks presented in preliminary and final rounds of year 2012 and 2013 World Body Painting Festival. For the selection of final coloring stimulation the most frequent coloring by theme was first chosen. Among them, 2 individual coloring bands were selected by theme among the high frequency colors. For the analysis of coloring image shown in body painting works total 8 coloring bands were created and they were compared and analyzed by indicating each divided coloring band on the coloring image scale by theme. In this research coloring image analysis was done after examining colors and coloring of artworks presented in World Body Painting Festival by theme. This research has its meaning that it provides information and guideline for coloring design work of body painting by analyzing coloring image used in color and coloring of body painting by theme.

• Korean Journal of Plant Resources
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• v.7 no.1
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• pp.35-44
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• 1994

The seasonal flower, leaf and fruit color characterlstics of deciduous woody landscape plants were investigated through the field survey in Suwon, Korea from January 1, 1992 toMarch 20, 1993.The results were as follows ;1. There were 12 cases in the combination of leaf spreading, anthesis, deblossom, fruit coloring,fruit falling, fall foliage coloring and leaf falling of deciduous woody landscape plants(163 spe-cies) investigated. And species of the leaf spreading, anthesis, deblossom, fall foliage coloringand leaf falling were 71(43.9%). And species of the leaf spreading, anthesis, deblossom,fruit coloring, fall foliage coloring, leaf falling and fruit falling were 40(24.5% ).2. The total continuing period of the flowering, fall foliage coloring and fruit coloring of decid-uous woody landscape plants(79 species) investigated varied from 2 months to more than 9months. And the species over 3 months below 4 months were 23(29.2%).3. There were 24 cases in the combination of color of flower, fall foliage and fruit of deciduouswoody landscape plants(79 species) investigated. And the species of the white flower, red fall fo-liage and red fruit were 16(20.3% ).

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1375-1377
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• 2002

New graph coloring problems are discussed as models of a multihop network in this report. We consider a total scheduling problem, and prove that this problem is NP-hard. We propose new scheduling models of a multi-hop network for CDMA system, and show the complexity results of the scheduling problems.