• 제목/요약/키워드: graph $(k_0,\

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ROMAN k-DOMINATION IN GRAPHS

  • Kammerling, Karsten;Volkmann, Lutz
    • 대한수학회지
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    • 제46권6호
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    • pp.1309-1318
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    • 2009
  • Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

THE PROBABILISTIC METHOD MEETS GO

  • Farr, Graham
    • 대한수학회지
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    • 제54권4호
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    • pp.1121-1148
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    • 2017
  • Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

결과 심각도 및 리스크 그래프에 기반한 철도 승강장 도어시스템의 안전 무결성 수준 할당 (Allocation of Safety Integrity Level for Railway Platform Screen Door System based on Consequence Severity and Risk Graph)

  • 송기태;이성일
    • 한국안전학회지
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    • 제30권6호
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    • pp.164-173
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    • 2015
  • There exists required safety integrity level (SIL) to assure safety in accordance with international standards for every electrical / electronics / control equipment or systems with safety related functions. The SIL is allocated from lowest level (level 0) to highest level (level 4). In order to guarantee certain safety level that is internationally acceptable, application of methodology for SIL allocation and demonstration based on related international standards is required. However, application standard differs from every industry in domestic or international for application on mythology for allocation and demonstration of SIL. Application or assessment is not easy since absence on clear criteria or common definition. This research studied not only fundamental concept of SIL required to guarantee safety in accordance with international standards for safety related equipment and system, but different types of methodologies for SIL allocation. Specifically, SIL allocation for Platform Screen Door system of railway is studied applying methodology of severity of accidents and risk graph among different methodologies for SIL allocation.

K-means 클러스터링을 이용한 케이블 접속재 계면결함의 부분방전 분포 해석 (Partial Discharge Distribution Analysis on Interlace Defects of Cable Joint using K-means Clustering)

  • 조경순;홍진웅
    • 한국전기전자재료학회논문지
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    • 제20권11호
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    • pp.959-964
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    • 2007
  • To investigate the influence of partial discharge(PD) distribution characteristics due to various defects on the power cable joints interface, we used the K-means clustering method. As the result of PD number(n) distribution analyzing on $\Phi-n$ graph, the phase angle($\Phi$) of cluster centroid shifted to $0^{\circ}\;and\;180^{\circ}$ increasing with applying voltage. It was confirmed that the PD quantify(q) and euclidean distance of centroid were increased with applying voltage from the centroid distribution analyzing of $\Phi-q$ plane. The dispersion degree was increased with calculated standard deviation of the $\Phi-q$ cluster centroid. The PD number and mean value on $\Phi-q$ graph were some different by electric field concentration with defect types.

TALYSURF에 의한 톱니의 마모량측정 (Measurement of Saw-Teeth Wear by TALYSURF)

  • 현정인;바니.크라메키
    • Journal of the Korean Wood Science and Technology
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    • 제8권1호
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    • pp.22-27
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    • 1980
  • Talysurf에 의한 톱니마모정도의 수량화가 수행되었다. (1)톱니의 단면은 아래식을 만족시키는 조건에서 Taysurf의 그래프로서 얻어진다. ${\frac{{\Delta}h}{h}}={\frac{V{\Delta}_x}{V_x}}$ {${\Delta}h$: stylus의 수직이동거리 h: 챠트에 있어서 수직거리 $V{\Delta}_x$: stylus의 이동속도 $V_x$: 챠트의 이동속도} (2) stylus의 오차는 아래식에 의하여 계산된다. i) 13.8${\mu}{\leqq}$x<20.4${\mu}$ y=-0.2246x+4.59${\mu}$ ii) 0${\leqq}$x<13.8${\mu}$ y=${\sqrt{(-18{\mu})^2-x^2}}-1.42x+32.7{\mu}}$ (3) 톱니단면과 stylus의 오차는 아래식에 의하여 계산된다. $E(%)=\frac{f(r){\times}{\frac{4}{18{\mu}}}}{f(R){\times}{\frac{R}{18.5{\mu}}}-f(r){\times}{\frac{r}{18{\mu}}}}{\times}100$ {E(%) : stylus의 오차/톱니의 둔함 r: stylus의 반경 R: 챠트에서 얻어지는 그라프의 반경 f(r): stylus의 오차 f(R): 챠트에서 얻어지는 그라프의 둔함} (4) 최대오차와 톱니단면의 관계에서 쌍곡선그라프를 얻을 수 있다.

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제한된 무선 자원 환경에 적합한 주파수 자동지정 알고리즘 (A Novel Frequency Allocation Algorithm for Limited Radio Resource Environments)

  • 구본홍;채찬병;박성호;박휘성;함재현
    • 한국통신학회논문지
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    • 제40권9호
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    • pp.1719-1721
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    • 2015
  • 주파수 자동지정 알고리즘은 빈번한 환경 변화에 따라 주파수 재지정이 요구되는 군용 통신에서 중요하게 고려되고 있다. 본 논문에서는 주파수 자동지정 문제를 그래프 이론 관점에서 해결한다. 그래프의 색칠 이론을 기반으로 한 알고리즘을 제시하여 기존의 탐욕 알고리즘 보다 사용되는 주파수 개수를 0.77배 감소시키는 성능 향상을 확인하였다. 또한, 주파수 범위와 재사용률 간의 맞교환을 통하여 원하는 성능을 얻을 수 있는 하이브리드 알고리즘을 제시하였다.

LINEAR ABSTRACT CAUCHY PROBLEM ASSOCIATED WITH AN EXPONENTIALLY BOUNDED C-SEMIGROUP IN A BANACH SPAC $E^*$

  • Ha, Ki-Sik;Kim, Jai-Heui;Kim, Jong-Kyu
    • 대한수학회보
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    • 제27권2호
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    • pp.157-164
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    • 1990
  • The purpose of this paper is to consider the inhomogeneous initial value problem (Fig.) in a Banach space X, where Z is the generator of an exponentially bounded C-semigroup in X, f9t) : [0, T].rarw.X and x.mem.X. Davies-Pang [1] showed the corresponding homogeneous equation, this is, the equation with f(t).iden.0, has a unique solution depending continuoously on the initial value x.mem.CD(z) in the $C^{-1}$-graph norm on CD(Z) when T=.inf..

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상수관망해석을 위한 도학의 적용 (Applications of Graph Theory for the Pipe Network Analysis)

  • 박재홍;한건연
    • 한국수자원학회논문집
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    • 제31권4호
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    • pp.439-448
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    • 1998
  • 대규모의 배수관망 시스템에서 유량해석을 위한 기법들이 많이 있지만 가장 널리 사용되고 있는 기법은 선형화 기법이다. 이 방법은 연속방정식과 에너지 방정식을 연립하여 해석하므로 이론적으로는 간단하나 실제 시스템에 적용을 위해서는 연립방정식 해석시 생성되는 계수매트릭스의 대각행력에 '0'이 발생하는 등 매우 큰 이산화된 계수 매트릭스의 처리가 문제가 되었다. 본 연구에서는 ill-condition 계수매트릭스의 발생을 배제하기 위해 도학이론으로부터 선형독립적인 폐합회로를 찾는 기법을 상수관망해석에 적용하여 선형화기법의 positive-definite 계수매트릭스를 만드는 기법을 개발하였다. 개발된 알고리듬의 적용성을 시험하고자 22개 가상관로 및 142개 관로를 가진 대구 인근의 실제 관망자료를 이용하여 유량해석을 실시하였다. 유량해석 결과 본 알고리듬이 적용된 모형에서는 가상관망 및 실제관로에서 수렴의 실패없이 원활하게 계산이 이루어지고 있었다. 본 연구결과는 관로내 정상상태 유량해석을 위해 효율적으로 이용될 것이 기대된다.

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Studies on Computer Optimization Techniques for Hydrophilic Vehicle Compositions

  • Lee, Chi-Ho;Shin, Young-Hee
    • Archives of Pharmacal Research
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    • 제11권3호
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    • pp.185-196
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    • 1988
  • The inflence of hydrophilic vehicles on percutaneous absorption rate of griseofulvin was studied using intact skin of full thickness of hairless rat. The in vitro absorption rates were used as the characteristics for deciding the optimum formula of ointment vehicles. The optimum formula of vehicle compositions for maximum absorption rate was obtained from the polynomial regression equation and the two graphical techniques, contour graph and partial derivative graph. It was composed of sodium lauryl sulfate (1.65 W /W%), white petrolatum (16.5 W /W%), propylene glycol (12.0 W /W%), and stearyl alcohol (19.6W /W%). The experimental value obtained from the optimum formula and the prediction value were 33.99 and 33.87 ${\mu}g/\sqrt{min}$, respectively. From these results, it was believed that optimum formula for semisolid dosage forms could be obtained from the application of the optimization technique used in this study.

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ON THE SIGNED TOTAL DOMINATION NUMBER OF GENERALIZED PETERSEN GRAPHS P(n, 2)

  • Li, Wen-Sheng;Xing, Hua-Ming;Sohn, Moo Young
    • 대한수학회보
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    • 제50권6호
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    • pp.2021-2026
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    • 2013
  • Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.