17 research outputs found

    Les revelations des particules legeres sur les reactions de fusion incomplete

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    SIGLECNRS T 56670 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

    New graphs related to (p,6) and (p,8)-cages

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    International audienceConstructing regular graphs with a given girth, a given degree and the fewest possible vertices is hard. This problem is called the cage graph problem and has some links with the error code theory. G-graphs can be used in many applications: symmetric and emisymmetric graph constructions, (Bretto and Gillibert (2008) [12]), hamiltonicity of Cayley graphs, and so on. In this paper, we show that G-graphs can be a good tool to construct some upper bounds for the cage problem. For p odd prime we construct (p, 6)-graphs which are G-graphs with orders 2p2 and 2p2 − 2, when the Sauer bound is equal to 4(p − 1)3. We construct also (p, 8)-G-graphs with orders 2p3 and 2p3 −2p, while the Sauer upper bound is equal to 4(p − 1)5

    G-graphs : a new representation of groups

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    AbstractAn important part of computer science is focused on the links that can be established between group theory and graph theory and graphs. Cayley graphs, that establish such a link, are useful in a lot of areas of sciences. This paper introduces a new type of graph associated with a group, the G-graphs, and presents many of their properties. We show that various characteristics of a group can be seen on its associated G-graph. We also present an implementation of the algorithm constructing these new graphs, an implementation that will lead to some experimental results. Finally we show that many classical graphs are G-graphs. The relations between G-graphs and Cayley graphs are also studied

    Aspect géométrique des groupes et des images (les G-graphes et la compression par hypergraphe)

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    CAEN-BU Sciences et STAPS (141182103) / SudocSudocFranceF

    Hypergraphs for Generic Lossless Image Compression

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    International audienceHypergraphs are a large generalisation of graphs; they are now used for many low-level image processing, by example for noise reduction, edge detection and segmentation [3, 4, 7]. In this paper we define a generic 2D and 3D-image representation based on a hypergraph. We present the mathematical definition of the hypergraph representation of an image and we show how this representation conducts to an efficient lossless compression algorithm for 2D and 3D-images. Then we introduce both 2D and 3D version of the algorithm and we give some experimental results on some various sets of images: 2D photo, 2D synthetic pictures, 3D medical images and some short animated sequences
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