• 한국콘텐츠학회논문지
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• 제14권10호
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• pp.840-849
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• 2014

본 연구는 알고리즘 학습을 초등학생에게 적용하여 알고리즘적 사고에 긍정적 효과가 있음을 보여준다. 알고리즘 학습에 대한 사전 경험이 없는 초등학교 6학년 35명을 대상으로 4주간 총 11회의 그래프 컬러링 문제를 활용한 알고리즘 학습을 실시하였다. 알고리즘 수업 후 학습자들의 알고리즘 흥미도와 절차적 사고능력의 변화를 검사하였다. 이와 같은 자료 분석을 통해 얻어진 연구 결과는 다음과 같다. 첫째, 알고리즘 흥미도의 하위요인인 알고리즘 학습 태도는 학습자에게 긍정적인 영향을 미치는 것으로 나타났다. 둘째, 그래프 컬러링을 활용한 알고리즘 학습은 학습자의 절차적 사고 능력을 향상시키는 것으로 나타났다. 따라서 알고리즘 학습은 초등학생의 절차적 사고 발달에 도움이 되며, 알고리즘 흥미도를 높이는 효과를 보여줌으로써 초등 교육 현장에서 알고리즘의 새로운 교육 방법을 제시하는데 의미가 있다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.1-6
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• 2014

Let G = (V ; E) be a simple undirected graph without loops and multiple edges, the vertex and edge sets of it are represented by V = V (G) and E = E(G), respectively. A weighting w of the edges of a graph G induces a coloring of the vertices of G where the color of vertex v, denoted $S_v:={\Sigma}_{e{\ni}v}\;w(e)$. A k-edge-weighting of a graph G is an assignment of an integer weight, w(e) ${\in}${1,2,...,k} to each edge e, such that two vertex-color $S_v$, $S_u$ be distinct for every edge uv. In this paper we determine an exact 3-edge-weighting of complete graphs $k_{3q+1}\;{\forall}_q\;{\in}\;{\mathbb{N}}$. Several open questions are also included.

• 대한수학회보
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• 제55권2호
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• pp.415-430
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• 2018

A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycle. A graph G is acyclically L-list colorable if for a given list assignment $L=\{L(v):v{\in}V(G)\}$, there exists an acyclic coloring ${\phi}$ of G such that ${\phi}(v){\in}L(v)$ for all $v{\in}V(G)$ A graph G is acyclically k-choosable if G is acyclically L-list colorable for any list assignment with $L(v){\geq}k$ for all $v{\in}V(G)$. Let G be a planar graph without 5-cycles and adjacent 4-cycles. In this article, we prove that G is acyclically 5-choosable if every vertex v in G is incident with at most one i-cycle, $i {\in}\{6,7\}$.

• 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.

• 대한수학회보
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• 제53권1호
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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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• 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.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.357-366
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• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• 한국통신학회논문지
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• 제38B권4호
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• pp.257-265
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• 2013

본 연구에서는 펨토 기지국 (Access Point: AP) 밀도가 높은 Orthogonal Frequency Division Multiple Access (OFDMA) 기반 펨토셀 네트워크 환경에서 하향링크 시스템 성능 향상을 위한 그래프 컬러링 기반 동적채널할당 (Graph Coloring based Dynamic Channel Assignment: GC-DCA) 방법을 연구한다. 제안하는 GC-DCA는 그래프 컬러링을 이용한 펨토 AP 그룹화 단계와 펨토 사용자 단말 (User Equipment: UE)의 신호 대 잡음비 (Signal to Interference plus Noise Ratio: SINR)을 고려한 동적채널할당 단계로 구성된다. 시뮬레이션을 통해 평균 펨토 UE 전송률과 펨토 UE 가 요구하는 전송률을 만족하지 못하는 펨토 UE 확률을 분석한 후, 제안하는 GC-DCA 가 다른 채널할당 방법들 보다 우수함을 보인다.

• 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.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.567-582
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• 2024

A total coloring of a graph G is an assignment of colors to the elements of a graphs G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G , denoted by χ''(G), is the minimum number of colors that suffice in a total coloring. In this paper, we proved the Behzad and Vizing conjecture for certain convex polytope graphs D^p_n, Q^p_n, R^p_n, E_n, S_n, G_n, T_n, U_n, C_n,respectively. This significant result in a graph G contributes to the advancement of graph theory and combinatorics by further confirming the conjecture's applicability to specific classes of graphs. The presented proof of the Behzad and Vizing conjecture for certain convex polytope graphs not only provides theoretical insights into the structural properties of graphs but also has practical implications. Overall, this paper contributes to the advancement of graph theory and combinatorics by confirming the validity of the Behzad and Vizing conjecture in a graph G and establishing its relevance to applied problems in sciences and engineering.