Geodesic
$\ell\sb 1$-rigid graphs
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 153-175.

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Summary: An $ell _{1}$-graph is a graph whose nodes can be labeled by binary vectors in such a way that the Hamming distance between the binary addresses is, up to scale, the distance in the graph between the corresponding nodes. We show that many interesting graphs are $ell _{1}$-rigid, i.e., that they admit an essentially unique such binary labeling.
Classification : 15, in, [4]), and, from, (i)
Keywords: $ell _{1}$-graph, cut cone, rigidity 
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     title = {$\ell\sb 1$-rigid graphs},
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Deza, M.; Laurent, M. $\ell\sb 1$-rigid graphs. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 153-175. http://geodesic.mathdoc.fr/item/JAC_1994__3_2_a3/