• 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|).

• 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.

• 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.

• 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.

• 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].

• 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 ${\Delta}(G){\geq}6$.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.149-156
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• 2006

The circular list coloring is a circular version of list colorings of graphs. Let $\chi_{c,l}$ denote the circular choosability(or the circular list chromatic number). In this paper, the circular choosability of outer planar graphs and odd wheel is discussed.

• The Journal of Advanced Prosthodontics
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• v.8 no.1
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• pp.37-42
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• 2016

PURPOSE. This study investigated the effect of amount of thickness reduction on color and translucency of dental monolithic zirconia ceramics. MATERIALS AND METHODS. One-hundred sixty-five monolithic zirconia specimens ($16.3mm{\times}16.3mm{\times}2.0mm$) were divided into 5 groups (Group I to V) according to the number of A2-coloring liquid applications. Each group was then divided into 11 subgroups by reducing the thickness up to 1.0 mm in 0.1-mm increments (Subgroup 0 to 10, n=3). Colors and spectral distributions were measured according to CIELAB on a reflection spectrophotometer. All measurements were performed on five different areas of each specimen. Color difference (${\Delta}E^*{^_{ab}}$) and translucency parameter (TP) were calculated. Data were analyzed using one-way ANOVA and multiple comparison $Scheff{\acute{e}}$ test (${\alpha}=.05$). RESULTS. There were significant differences in CIE $L^*$ between Subgroup 0 and other subgroups in all groups. CIE $a^*$ increased (0.52<$R^2$<0.73), while CIE $b^*$ decreased (0.00<$R^2$<0.74) in all groups with increasing thickness reduction. Perceptible color differences (${\Delta}E^*{^_{ab}}$>3.7) were obtained between Subgroup 0 and other subgroups. TP values generally increased as the thickness reduction increased in all groups ($R^2$>0.89, P<.001). CONCLUSION. Increasing thickness reduction reduces lightness and increases a reddish, bluish appearance, and translucency of monolithic zirconia ceramics.

• Mass Spectrometry Letters
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• v.14 no.2
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• pp.42-47
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• 2023

Carthamus tinctorius L. (known as safflower) is a valuable oil plant whose importance is increasing rapidly in the world due to its high adaptation to arid regions. The seeds of this unique plant are especially used in edible oil, soap, paint, varnish and lacquer production. Its flowers are used in vegetable dye production and medicinal purposes beside its features as a coloring and flavoring in food. After the oil is removed, the remaining pulp and plant parts are used as animal feed, and dry straw residues are used as fuel. Beside all these features, its usage as a herbal medicinal plants for various diseases has gained importance on recent years. In this study, it was designed a plant metabolomic approach which transfers all the recent data processing strategies of untargeted metabolomics in clinical applications to the present study. Q-TOF LC/MS-based analysis of the extracts (70% ethanol, hexane, and chloroform) for both seed and flowers was performed using a C18 column (Agilent Zorbax 1.8 µM, 100 × 2.1 mm). Differences were observed in seed and fruit extracts and these differences were visualized using principal component analysis (PCA) plots. The total number and intersections of the peaks in the extracts were visualized using peak count comparison graph. Based on the experimental results, the number of the detected peaks for seeds was higher than the ones for the flowers for all solvent systems to extract the samples.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.999-1007
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.