The distinguishing index of the Cartesian product of countable graphs
Broere, Izak ; Pilśniak, Monika
ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016), / Harvested from ARS MATHEMATICA CONTEMPORANEA
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The distinguishing index D′(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is preserved only by the trivial automorphism.We derive some bounds for this parameter for infinite graphs. In particular, we investigate the distinguishing index of the Cartesian product of countable graphs.Finally, we prove that Dʹ(K2ℵ0) = 2, where K2ℵ0 is the infinite dimensional hypercube.

Publié le : 2016-01-01
DOI : https://doi.org/10.26493/1855-3974.792.403 
@article{792,
     title = {The distinguishing index of the Cartesian product of countable graphs},
     journal = {ARS MATHEMATICA CONTEMPORANEA},
     volume = {12},
     year = {2016},
     doi = {10.26493/1855-3974.792.403},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/792}
}

Broere, Izak; Pilśniak, Monika. The distinguishing index of the Cartesian product of countable graphs. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.792.403. http://gdmltest.u-ga.fr/item/792/