• 디지털융복합연구
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• 제20권2호
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• pp.345-351
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• 2022

단순 무방향 그래프 G 의 L(2,1)-coloring은 d(u,v)가 두 정점 사이의 거리일 때 두 가지 조건 (1) d(x,y) = 1 라면 |f(x)-f(y)|≥ 2, (2) d(x,y) = 2 라면 |f(x)-f(y)|≥ 1 을 만족하는 함수 f : V → [0,1,…,k]를 정의하는 것이다. 임의의 L(2,1)-coloring c 에 대하여 G 의 c-span 은 λ(c)=max{|c(u)-c(v)|| u,v∈V} 이며, L(2,1)-coloring number 인 λ(G)는 모든 가능한 c 에 대하여 λ(G) = min{λ(c)} 로 정의된다. 본 논문에서는 Harary의 정리에 기반하여 지름이 2인 그래프에 대하여 여그래프에 해밀턴 경로의 존재여부를 Tabu Search를 사용해 판단하고 이를 통해 λ(G)가 n(=|V|)과 같음을 분석한다.

• 대한수학회보
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• 제59권1호
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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.

• 한국콘텐츠학회논문지
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• 제8권5호
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• pp.52-60
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• 2008

위성 통신 분야에서 널리 사용되는 시분할 다중 스위칭 시스템은 많은 저대역폭 가입자들로부터 발생되는 트랙픽을 반복되는 프레임에 타임 슬롯을 할당해야 한다. 본 논문에서는 타임 슬롯 할당을 위한 새로운 방법을 제안한다. 기존의 방법인 네트워크 흐름 모델을 사용하지 않고 새로운 방법인 그래프 채색방법을 사용하여 효율적인 타임 슬롯 할당 알고리즘을 제안하였다. 제안된 알고리즘은 주어진 트래픽의 프레임 길이가 2의 멱승일 경우 트래픽을 정확히 반으로 나누어 할당한다. 분할된 트래픽의 프레임 길이가 1이 될 때까지 이 과정을 계속적으로 반복해 분할한다. 제안된 알고리즘의 시간 복잡도는 프레임의 길이가 L이고 스위치 크기가 N인 경우에는 기존의 네트워크 흐름 모델을 사용한 최적의 타임 슬롯 할당 알고리즘의 시간 복잡도는 $O(N^{4.5})$ 인데 반해 $O(NLlog_2L)$이다.

• 대한치과보철학회지
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• 제55권1호
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• pp.18-25
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• 2017

목적: 이 연구의 목적은 coloring agent의 종류와 적용 횟수가 지르코니아의 색조에 미치는 영향을 알아보는 것이다. 재료 및 방법: 단일구조 지르코니아($15.7mm{\times}15.7mm{\times}2.0mm$)를 준비하여 완성된 시편은 11개 실험군 그룹으로 coloring agent의 종류와 적용 횟수에 따라 a1-a5와 w1-w5로 나누었다. 색조의 측정은 분광측색기를 이용하여 이루어졌다. Coloring agent를 적용시키지 않은 그룹을 대조군으로 설정하였다. 각 그룹의 색차의 정도(${{\Delta}E^*}_{ab}$)와 translucency parameter (TP)를 분석하였다. 측정치는 two-way ANOVA, multiple comparison $Sch{\acute{e}}ffe$ test, Pearson correlation와 linear regression analysis를 이용하여 분석하였다. 결과: Coloring agent의 적용횟수가 증가할수록 두가지 종류 모두에서 지르코니아의 명도는 감소하고 황색계열은 증가했다. Coloring agent는 지르코니아의 투명도에는 영향을 미치지 않았다. 각 그룹 간의 색조차이는 ${0.87{\Delta}E^*}_{ab}$에서 ${9.43{\Delta}E^*}_{ab}$였다. 결론: Coloring agent의 종류와 적용 횟수는 지르코니아의 색조 차이에 영향을 미치지 않았다.

• 대한수학회보
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• 제50권4호
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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].

• 대한수학회보
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• 제49권2호
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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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• 제20권1_2호
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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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• 제8권1호
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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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• 제14권2호
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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.

• 한국정보과학회논문지:시스템및이론
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• 제26권8호
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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.