Broere, IzakPilsniak, Monika2015-06-222015-06-222015-03-30Broere, I & Pilsniak, M 2015, 'The distinguishing index of infinite graphs', The Electronic Journal of Combinatorics, vol. 22, no. 1, pp. 1-10.1077-8926 (online)http://hdl.handle.net/2263/45651The distinguishing index D0(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number D(G) of a graph G, which is defined with respect to vertex colourings. We derive several bounds for infinite graphs, in particular, we prove the general bound D0(G) 6 (G) for an arbitrary infinite graph. Nonetheless, the distinguish- ing index is at most two for many countable graphs, also for the infinite random graph and for uncountable tree-like graphs. We also investigate the concept of the motion of edges and its relationship with the Infinite Motion Lemma.enResearch School of Computer Science at the Australian National UniversityDistinguishing indexAutomorphismInfinite graphCountable graphEdge colouringInfinite Motion LemmaArticle