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On the Existence of $t$-Identifying Codes in Undirected De Bruijn Graphs | | Victoria Horan
; | | Date: |
3 Aug 2015 | | Abstract: | This paper proves the existence of $t$-identifying codes on the class of
undirected de Bruijn graphs with string length $n$ and alphabet size $d$,
referred to as $mathcal{B}(d,n)$. It is shown that $mathcal{B}(d,n)$ is
$t$-identifiable whenever $d geq 3$ and $n geq 2t$, and $t geq 1$. We also
show that $mathcal{B}(d,n)$ is $t$-identifiable if either $d geq 3$, $n geq
3$, and $t=2$, or if $d = 2$, $n geq 3$, and $t=1$. The remaining cases remain
open. Additionally, we show that the eccentricity of the undirected non-binary
de Bruijn graph is $n$. | | Source: | arXiv, 1508.0403 | | Services: | Forum | Review | PDF | Favorites | |
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