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In the parallel processing field, graph embedding is motivated by simulationinterconnection networks to another. The quadtree is an important techniqueused to present spatial data and is used in many application domains,especially computer vision and image processing. Researchers are interested inthe construction and manipulation of quadtrees on parallel machines. Thecrossed cubes consider an alternative to the ordinary hypercube. It offers manyattractive properties. Significantly, it reduces diameter by a factor of 2 thatof the ordinary cubes. Moreover, the crossed cubes have a great capacity tosimulate other architectures. This paper is interested in the one-by-onedilation two embedding of a particular sub-quadtree graph into m-dimensionalcrossed cubes.

Dilation two embedding one-by-one particular sub-quadtree into M-dimentional crossed cubes