• Journal of Digital Convergence
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• v.20 no.2
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• pp.345-351
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• 2022

For simple undirected graph G=(V,E), L(2,1)-coloring of G is a nonnegative real-valued function f : V → [0,1,…,k] such that whenever vertices x and y are adjacent in G then |f(x)-f(y)|≥ 2 and whenever the distance between x and y is 2, |f(x)-f(y)|≥ 1. For a given L(2,1)-coloring c of graph G, the c-span is λ(c) = max{|c(v)-c(v)||u,v∈V}. L(2,1)-coloring number λ(G) = min{λ(c)} where the minimum is taken over all L(2,1)-coloring c of graph G. In this paper, based on Harary's Theorem, we use Tabu Search to figure out the existence of Hamiltonian Path in a complementary graph and confirmed that if λ(G) is equal to n(=|V|).

• 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 applied mathematics & informatics
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• v.41 no.3
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• pp.511-524
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• 2023

An L(p₁, p₂, p₃, . . . , p_m)-labeling of a graph G is an assignment of non-negative integers, called as labels, to the vertices such that the vertices at distance i should have at least pi as their label difference. If p₁ = 4, p₂ = 3, p₃ = 2, p₄ = 1, then it is called a L(4, 3, 2, 1)-labeling which is widely studied in the literature. A L(4, 3, 2, 1)-path coloring of graphs, is a labeling g : V (G) → Z⁺ such that there exists at least one path P between every pair of vertices in which the labeling restricted to this path is a L(4, 3, 2, 1)-labeling. This concept was defined and results for some simple graphs were obtained by the same authors in an earlier article. In this article, we study the concept of L(4, 3, 2, 1)-path coloring for complete bipartite graphs, 2-edge connected split graph, Cartesian product and join of two graphs and prove an existence theorem for the same.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.119-139
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• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1303-1314
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• 2013

An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors. A graph G is said to be injectively $k$-choosable if any list $L(v)$ of size at least $k$ for every vertex $v$ allows an injective coloring ${\phi}(v)$ such that ${\phi}(v){\in}L(v)$ for every $v{\in}V(G)$. The least $k$ for which G is injectively $k$-choosable is the injective choosability number of G, denoted by ${\chi}^l_i(G)$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G)={\Delta}(G)$. Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < $\frac{8k-3}{3k}$, then ${\chi}^l_i(G)={\Delta}(G)$ where $k={\Delta}(G)$ and ${\Delta}(G){\geq}6$. In addition, when ${\Delta}(G)=5$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{17}{7}$, and when ${\Delta}(G)=4$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{7}{3}$. These results generalize some of previous results in [1, 4].

• Horticultural Science & Technology
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• v.28 no.5
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• pp.757-761
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• 2010

This research was conducted to investigate effect of ethephon on fruit enlargement and coloring of 'Fuyu' persimmon ($Diospyros$ $kaki$). At 7 weeks after ethephon treatment, fruit weight and diameter became significantly heavier and longer in 80 and $100mg{\cdot}L^{-1}$ than the other concentrations of ethephon. Fruit peel hardness decreased with increasing ethephon concentration. The decreased levels were apparent with the treatments beyond $40mg{\cdot}L^{-1}$ at the beginning, and then with those beyond $60mg{\cdot}L^{-1}$. Hunter $a^*$ and $Chroma^*$ of fruit peel treated with ethephon over $20mg{\cdot}L^{-1}$ were significantly higher compared to those with control ($0mg{\cdot}L^{-1}$), but there were no significant differences among those with the ethephon treatments over $20mg{\cdot}L^{-1}$. The increased levels of the $Chroma^*$ were apparent with the treatments beyond $60mg{\cdot}L^{-1}$ at the beginning and then with those of 20 and $40mg{\cdot}L^{-1}$. ${\beta}$-Carotene and lycopene contents of fruit peel were higher with the ethephon treatment beyond $40mg{\cdot}L^{-1}$. Although the ethephon application at 20 and $40mg{\cdot}L^{-1}$ had no effects on fruit enlargement, but fruit coloring was advanced by 2 weeks with the application at $40mg{\cdot}L^{-1}$.

• The Journal of Korean Academy of Prosthodontics
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• v.55 no.1
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• pp.18-25
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• 2017

Purpose: The aim of this study was to evaluate the effect of two types of coloring agents and the number of application on the color of zirconia. Materials and methods: Monolithic zirconia specimens ($15.7mm{\times}15.7mm{\times}2.0mm$) (n = 33) was prepared and divided into 11 groups. Each experimental group was coded as a1-a5, w1-w5 according to the type of coloring agent and number of application. Specimens with no coloring agent applied were set as control group. The color difference of specimen was measured by using double-beam spectrophotometer, and calculated color difference (${{\Delta}E^*}_{ab}$), translucency parameter (TP). All data was analyzed with two-way ANOVA, multiple comparison $Sch{\acute{e}}ffe$ test, Pearson correlation and linear regression analysis. Results: As the number of application increased, values of $CIE\;L^*$ was decreased, but values of $CIE\;b^*$ was increased in both coloring agents. However, there was no significant difference on values of translucency parameter. The color difference range of each group was ${0.87{\Delta}E^*}_{ab}$ to ${9.43{\Delta}E^*}_{ab}$. Conclusion: In this study, type of coloring agent and the number of application did not affect the color difference of zirconia.

• The Journal of the Korea Contents Association
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• v.8 no.5
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• pp.52-60
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• 2008

A simple Time Division Multiplex(TDM) switching system which has been widely in satellite networks provides any size of bandwidth for a number of low bandwidth subscribers by allocating proper number of time slots in a frame. In this paper, we propose a new approach based on graph coloring model for efficient time slot assignment algorithm in contrast to network flow model in previous works. When the frame length of an initial matrix of time slot requests is 2's power, this matrix is divided into two matrices of time slot requests using binary divide and conquer method based on the graph coloring model. This process is continued until resulting matrices of time slot requests are of length one. While the most efficient algorithm proposed in the literature has time complexity of $O(N^{4.5})$, the time complexity of the proposed algorithm is $O(NLlog_2L)$, where N is the number of input/output links and L is the number of time slot alloted to each link in the frame.

• Journal of Technologic Dentistry
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• v.35 no.3
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• pp.193-200
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• 2013

Purpose: In this study, in order to provide objective standard of the mixed concentration of the zirconia coloring-liquids, compare the shade differences after colored zirconia blocks from different concentrations. Methods: After immersion for 2 minutes zirconia specimen ($1.5{\times}1.5{\times}0.6{\pm}0.01mm$) in coloring-liquids that produced different concentrations, were sintered in furnace dedicated. Then, it was measured in spectrophotometer and Shadepilot. It has been determined mean and standard deviation of the color difference for each group, and verified by one-way ANOVA using the (version12.0) SPSS WIN Program the difference in shade according to the concentration at the significance level of 95% confidence, it conducted a Tukey's multiple range test to post-test. Results: The mean of $L^*$ was decreased toward LN35 group, however the mean of $a^*$ and $b^*$ was increased(p<.05). There is a statistically significant difference in the results of $L^*$ post hoc test of each group was LN15-LN30/LN35, LN20-LN30/LN35, LN25-LN30/LN35, and LN30-LN35 group. The $a^*$ group, it was found that there is a statistically significant difference in all groups for each(p<.05). The $b^*$ group, it was found that there is a statistically significant difference in all groups except the LN25-LN30(p<.05). Conclusion: In order to make effective use of the coloring-liquids of zirconia, the device objective, accurate concentration measurement is required, from the present study, we presented evidence basic to this.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.359-365
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• 2012

Giving a planar graph G, let $x^'_l(G)$ and $x^{''}_l(G)$ denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if a planar graph G without 6-cycles with chord, then $x^'_l(G){\leq}{\Delta}(G)+1$ and $x^{''}_l(G){\leq}{\Delta}(G)+2$ where ${\Delta}(G){\geq}6$.