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Cited by 19 publications
(17 citation statements)
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“…This goes similarly as in Theorem 2 using the correspondence of a vertex (i, j) in the king grid K and the vertex i + j · d (mod n) in the circulant graph C n (1, d − 1, d, d + 1). The case of self-identifying codes is again easier than in Theorem 2, since it suffices, as discussed in [12], to check the situation for d(x, y) = 1 (as other cases follow).…”
Section: Infinite Grids and Circulant Graphsmentioning
confidence: 99%
See 1 more Smart Citation
“…This goes similarly as in Theorem 2 using the correspondence of a vertex (i, j) in the king grid K and the vertex i + j · d (mod n) in the circulant graph C n (1, d − 1, d, d + 1). The case of self-identifying codes is again easier than in Theorem 2, since it suffices, as discussed in [12], to check the situation for d(x, y) = 1 (as other cases follow).…”
Section: Infinite Grids and Circulant Graphsmentioning
confidence: 99%
“…Indeed, if C is an identifying code in a graph G = (V, E), then we can locate one irregularity (for example, a fire or an intruder) in G as all the identifying sets are distinct. However, if there are more than one irregularity in G, then we can mislocate the irregularity (see [12]), since we could have I(C; u) = I(C; v 1 ) ∪ I(C; v 2 ) for some vertices u, v 1 , v 2 ∈ V , and more disturbingly not even notice that something is wrong. Thus, to locate one irregularity and detect multiple ones, the following definition of self-identifying codes have been introduced in [12] (although in the paper the code is called 1 + -identifying).…”
mentioning
confidence: 99%
“…The following result from [15] turns out to be useful in what follows when we bound from below the density of a code.…”
Section: Codes With T =mentioning
confidence: 99%
“…The formal definition of self-identifying codes is given as follows. In addition to [11], self-identifying codes have also been previously discussed in [13,14]. In these papers, two useful characterizations have been presented for self-identifying codes.…”
Section: Introductionmentioning
confidence: 99%