• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.511-520
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• 2024

In this paper, we introduce the concept of split and non-split tree (D, C)- set of a connected graph G and its associated color variable, namely split tree (D, C) number and non-split tree (D, C) number of G. A subset S ⊆ V of vertices in G is said to be a split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is disconnected. The minimum size of the split tree (D, C) set of G is the split tree (D, C) number of G, γ_χST (G) = min{|S| : S is a split tree (D, C) set}. A subset S ⊆ V of vertices of G is said to be a non-split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is connected and non-split tree (D, C) number of G is γ_χST (G) = min{|S| : S is a non-split tree (D, C) set of G}. The split and non-split tree (D, C) number of some standard graphs and its compliments are identified.

• 대한수학회논문집
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• 제27권4호
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• pp.843-849
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• 2012

Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${\chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.49-60
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• 2016

In this paper, two different approaches to chromatic number of a bipolar fuzzy graph are introduced. The first approach is based on the α-cuts of a bipolar fuzzy graph and the second approach is based on the definition of Eslahchi and Onagh for chromatic number of a fuzzy graph. Finally, the bipolar fuzzy vertex chromatic number and the edge chromatic number of a complete bipolar fuzzy graph, characterized.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.425-437
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• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• 복식
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• 제59권4호
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• pp.67-81
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• 2009

This study aims to characterize the effect of different combinations of chromatic-achromatic colors and 1:2:3 area-ratio variation of stripe necktie, and gender on the image of male wearer. The experimental materials developed for this study are a set of stimuli and response scales. The stimuli consist of 84 color pictures manipulated with every combination of 12 different colors and 7 different area-ratio. The 7-point scale designed for visual evaluation of image formation included 26 bipolar adjectives. The subjects were 2016 undergraduate students in Gyeongnam, Seoul, Busan, and Daegu areas. The results of this study were as follows. The analyses of images of male wearer in terms of combinations of chromatic-achromatic colors and I :2:3 area-ratio variation of oblique stripe necktie reveal that the concerned factors are of five characteristic dimensions of youth-activity, ability, attractiveness, appeal, and warmness. In addition, it has been found that individual images of male wearer are affected by observer's gender as well as combinations of chromatic-achromatic colors and 1:2:3 area-ratio variation of stripe neckties and that those images vary with every combination of each factor. The study results are highly expected to be used as useful sources in developing necktie designs.

• 한국의상디자인학회지
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• 제12권3호
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• pp.133-143
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• 2010

The purpose of this study was to investigate the clothing image according to gender, coloration of chromatic and achromatic color, and interval of checked pattern. The experimental materials developed for this study were a set of stimulus and response scales. The stimuli were 16 color pictures, in which the gender(male, female), interval(0.5cm, 1.5cm, 3.5cm, 5.5cm), and coloration(WR: white+red, WY: white+yellow, WB: white+Blue, WP: white+purple) were manipulated. The 7-point scale was used for evaluation of clothing image. Data were obtained from 192 male college students and 192 female college students living in Seoul, Gwangju, Daegu, Jinju, and Changwon on March 2010. For data analysis, ANOVA and Duncan-test were used by using SPSS program. Results of this study were as follows.; Clothing image according to coloration of chromatic and achromatic color, and interval of checked pattern consisted of six dimensions of attractiveness, appeal, activity, freshness, modesty, and cuteness. Gender showed an independent effect on attractiveness, appeal, activity, freshness, and cuteness. Interval showed an independent effect on attractiveness. Coloration showed an independent effect on appeal, activity, freshness, modesty, and cuteness. Also, interaction effects of gender and coloration on freshness and cuteness were found.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.

• 감성과학
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• 제11권3호
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• pp.325-338
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• 2008

본 연구는 남녀 대학생을 대상으로 유채-무채 배색, 면적비, 성별이 남성복 착용자의 이미지에 미치는 영향을 규명하고자 한다. 이들 단서로 사용된 84개의 자극물에 대한 이미지를 평가하기 위해 경남, 서울, 부산, 대구 등지에 거주하는 남녀 대학생 2016명의 피험자를 대상으로 하였으며 26쌍의 의미미분척도를 요인 분석하여 이미지 차원을 밝혔다. 그 결과 이들 단서들이 어떻게 조합되어 이미지에 영향을 미치는지 규명하였으며 다음과 같은 결론을 얻었다. 유채-무채 배색, 면적비, 성별에 따른 3색 사선 스트라이프 넥타이 착용자의 이미지 차원은 젊음.활동성, 능력성, 매력성, 현시성, 온유성의 5개 차원으로 도출되었으며, 유채-무채 배색, 면적비, 지각자의 성별이 이미지 형성에 미치는 영향은 이미지 차원에 따라 차이를 나타내었다. 이러한 연구결과는 넥타이 디자인 기획 시 소비자의 감성을 충족시킬 수 있는 자료제시가 될 것으로 본다.

• 한국생활과학회지
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• 제16권5호
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• pp.1007-1019
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• 2007

The purpose of this study is to investigate the effect of achromatic shirt and chromatic tie combination on image of menswear. This experiment was designed by shirt color(N9, N7, N4, N2), tie color(red, orange, yellow, green, blue, purple), tie tone(vivid, light, dull, dark), and perceiver gender(a male, a female). The experimental materials developed for this study were a set of stimulus and response scales. The stimuli were 96 upper body photographs and 26 7-point bi-polar adjectives were used to evaluate the image. The subjects of this research were 480 male and 480 female college students. The data was analyzed by using SPSS program. Analysis methods were four-way ANOVA. The items of the adjectives were classified into 4 image factor: potency, activity, attractiveness, and visibility. Shirt color, tie color, tie tone influenced on the 4 image dimension greatly by interaction as well as independently. Dull or dark tone tie had an effect on the formation of potency image. And white color shirt, vivid or light tone tie had an effect on the formation of activity image. White or black shirt had a positive effect on attractiveness, and black shirt or vivid tone tie was effective for visible image.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.