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El diámetro de ciertos digrafos circulantes de triple paso.

Paz Morillo Bosch, Miguel Angel Fiol Mora (1986)

Stochastica

This paper studies some diameter-related properties of the 3-step circulant digraphs with set of vertices V≡ZN and steps (± a,b). More precisely, it concentrates upon maximizing their order N for any fixed value of their diameter k. In the proposed geometrical approach, each digraph is fully represented by a T-shape tile which tessellates periodically the plane. The study of these tiles leads to the optimal solutions.

Embedding complete ternary trees into hypercubes

S.A. Choudum, S. Lavanya (2008)

Discussiones Mathematicae Graph Theory

We inductively describe an embedding of a complete ternary tree Tₕ of height h into a hypercube Q of dimension at most ⎡(1.6)h⎤+1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Tₕ into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Tₕ into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log₂3)h⎤ ( = ⎡(1.585)h⎤) or ⎡(log₂3)h⎤+1....

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