The distinguishing index of the Cartesian product of countable graphs
Izak Broere, Monika Pilśniak · Ars Mathematica Contemporanea · 2016
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.