Geodesic
Identifying codes of Cartesian product of two cliques of the same size
The electronic journal of combinatorics, Tome 15 (2008)
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We determine the minimum cardinality of an identifying code of $K_n\square K_n$, the Cartesian product of two cliques of same size. Moreover we show that this code is unique, up to row and column permutations, when $n\geq 5$ is odd. If $n\geq 4$ is even, we exhibit two distinct optimal identifying codes.
DOI : 10.37236/879
Classification : 05C76, 05C69, 94B60, 94C12
Mots-clés : identifying code, clique product, Cartesian product 
@article{10_37236_879,
     author = {S. Gravier and J. Moncel and A. Semri},
     title = {Identifying codes of {Cartesian} product of two cliques of the same size},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/879},
     zbl = {1180.05088},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/879/}
}
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S. Gravier; J. Moncel; A. Semri. Identifying codes of Cartesian product of two cliques of the same size. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/879

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