Geodesic
On recursively directed hypercubes
The electronic journal of combinatorics, Tome 9 (2002)

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Zbl EuDML
In this paper we introduce the recursively directed hypercubes, and analyze some of their structural properties. We show that every recursively directed hypercube is acyclic, and has a unique pair of source and sink nodes. The main contribution of the paper is an analysis of distances between the nodes in such a graph. We show that the distance from the source node to any other node, and from any node to the sink node is bounded by $n+1$, where $n$ is the dimension of the hypercube, but the diameter of a recursively directed hypercube may be exponential in $n$.
DOI : 10.37236/1640
Classification : 05C62, 05C12, 91B08, 05C38
Mots-clés : recursively directed hypercubes, distances, diameter 
Carmel Domshlak. On recursively directed hypercubes. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1640
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     author = {Carmel Domshlak},
     title = {On recursively directed hypercubes},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1640},
     zbl = {0995.05103},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1640/}
}
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