Geodesic
The distinguishing index of the Cartesian product of countable graphs
Ars Mathematica Contemporanea, Tome 13 (2017) no. 1, pp. 15-21.

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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.
DOI : 10.26493/1855-3974.792.403
Keywords: Distinguishing index, automorphism, infinite graph, edge colouring, infinite dimensional hypercube 
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Izak Broere; Monika Pilśniak. The distinguishing index of the Cartesian product of countable graphs. Ars Mathematica Contemporanea, Tome 13 (2017) no. 1, pp. 15-21. doi : 10.26493/1855-3974.792.403. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.792.403/

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