• 호남수학학술지
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• 제32권4호
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• pp.769-776
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• 2010

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. For a connected graph G, $G^p$ (p > 1) is the graph obtained from G by adding the edges (u, v) to G whenever 2 $\leq$ dist(u, v) $\leq$ p in G. And the pebbling exponent of a graph G to be the least power of p such that the pebbling number of $G^p$ is equal to the number of vertices of G. We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.

• 대한수학회논문집
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• 제30권1호
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• pp.45-64
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• 2015

In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak [15] first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus 3. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We prove that these graphs satisfy the conjecture.

• 대한산업공학회지
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• 제20권3호
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• pp.3-14
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• 1994

In this study, two reliability computational algorithms which respectively utilize a factoring method are proposed for a system represented by reliability block diagram. First, vertex factoring algorithm is proposed. In this algorithm, a reliability block diagram is considered as a network graph with vertex reliabilities. Second algorithm is mainly concerned with conversion of a reliabilities block diagram into a network graph with edge reliabilities. In this algorithm, the independence of edges is preserved by eliminating replicated edges, and in computing the reliability of a converted network graph, existing edge factoring algorithm is applied. The efficiency of two algorithms are compared for example systems with respect to computing times. The results shows that the second algorithm is shown to be more efficient than the first algorithm.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.41-44
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• 2001

삼각형 메쉬(triangular mesh)로 이루어진 삼차원 영상의 큰 데이터량을 줄이기 위한 메쉬 부호화의 연구가 활발히 진행되고 있다. 그리고, 최근에는 삼차원 부호화 데이터의 네트워크 전송 문제가 대두되어, 점진적 부호화(proressive mesh compression)에 대한 알고리듬들도 제안되고 있다. 본 논문은 꼭지점의 위치 정보 및 간략화 과정의 꼭지점 패턴(vertex pattern) 규칙을 이용하여, 기존의 점진적 부호화 알고리듬의 부호화 성능을 개선한 알고리듬을 제안한다. 꼭지점의 위치 정보를 이용하여 기존의 알고리듬에 비해 낮은 엔트로피(entropy)를 얻었으며, 꼭지점 패턴 정보를 이용하여 복원시 분할 꼭지점(split vertex)의 탐색 범위를 한정하였다. 전산 모의 실험을 통해, 제안하는 알고리듬이 기존의 점진적 메쉬 부호화 연구에 비해, 연결 정보 부호화에서 대략 30%정도 향상된 부호화 성능을 가짐을 확인할 수 있었다.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표논문집(II)
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.16.1-16
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• 2003

A subset S of vertices of a graph G is independent if no two vertices of S are adjacent by an edge in G. Also we say that S is maximal independent if it is contained In no larger independent set in G. A planted plane tree is a tree that is embedded in the plane and rooted at an end-vertex. A (k＋1) -valent tree is a planted plane tree in which each vertex has degree one or (k＋1). We classify maximal independent sets of (k＋1) -valent trees into two groups, namely, type A and type B maximal independent sets and consider specific independent sets of these trees. We study relations among these three types of independent sets. Using the relations, we count the number of all maximal independent sets of (k＋1) -valent trees with n vertices of degree (k＋1).

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.189-200
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• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2001년도 정기총회 및 학술대회
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• pp.213-218
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• 2001

본 논문에서는 파동분할(Wavepartitioning) 방식을 기반으로 꼭지점들간의 특징적인 관계(Vertex Pedigree)를 이용한 순차적(Sequential) 메쉬 부호화 방식을 제안한다. 파동분할 방식은 호수에 물방울이 퍼져 나가는 자연 원리를 이용하여 초기 삼각형의 주위에 삼각형을 덧붙여 가면서 하나의 SPB(Small Processing Block)을 만들어내는 방식이다. 이 방식을 이용하여 하나의 모델을 서로 독립적인 SPB로 분할하고, 각각의 SPB내에서 초기 삼각형을 중심으로 그것에 덧붙여진 삼각형에 의해 만들어진 원 또는 반원을 찾는다. 또한, 그 원주를 따라 순차적으로 꼭지점을 구하면 각각의 꼭지점들은 서로의 관계에 따라 일정한 패턴으로 늘어서게 되고, 이것을 이용하여 연결성 정보 없이 부가 정보만으로 모델을 순차적으로 무손실 부호화한다.

• 한국정밀공학회지
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• 제23권3호
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• pp.102-109
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• 2006

Several methods for PCB pattern inspection have been tried to detect fine detects in pad contours, but their low detection accuracy results from pattern variations originating from etching, printing and handling processes. The adaptive inspection algorithm has been newly proposed to extract minute defects based on movable segments. With gerber master images of PCB, vertex extractions of a pad boundary are made and then a lot of segments are constructed in master data. The pad boundary is composed of segment units. The proposed method moves these segments to optimal directions of a pad boundary and so adaptively matches segments to pad contours of inspected images, irrespectively of various pattern variations. It makes a fast, accurate and reliable inspection of PCB patterns. Its performances are also evaluated with several images.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.513-522
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• 1994

A multi-dimensional design is most easily constructed via the amalgamation of one-dimensional component block designs. However, not all sets of component designs are compatible to be amalgamated. The conditions for compatibility are related to the concept of a complete matching in a graph. In this paper, we give sufficient conditions for unequal-replicate designs. Two types of conditions are proposed; one is based on the number of verices adjacent to at least one vertex and the other is ona a degree of vertex, in a bipartite graph. The former is an extension of the sufficient conditions of equal-replicate designs given by Dean an Lewis (1988).