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ON DOMINATION NUMBERS OF GRAPH BUNDLES
Zmazek, Blaz,Zerovnik, Janez 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.
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A. Trkov,I. Kodeli,G. Zerovnik,R. Capote,D. W. Muir 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.59 No.23
Taking the FNG-W benchmark with a D-T source in front of a large tungsten block as an example, the impact of the reaction cross-section covariance data on the predicted activities of monitor foils inside the block and the associated uncertainties were studied. Cross-material covariances between the isotopic cross sections of tungsten were obtained by including experimental measurements of the elemental total cross sections above the resonance range. Cross-material covariances of the elastic and the radiative capture reactions were considered. Since the original cross sections were evaluated accurately from the reasonably abundant isotopic data, the impact of introducing elemental data on the isotopic cross sections and their uncertainties were small. Correlations were observed mainly in the elastic channel, which has a relatively low sensitivity to the calculated monitor activities of the benchmark. Consequently, the impact on the predicted monitor sample activities was also small in terms of the absolute value and the uncertainty. The main achievement of the work was the demonstrated data consistency and the development of tools for including elemental data in isotopic cross section evaluation and the evaluation of cross-material covariances.
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