AbstractThe distinguishing indexD′(G)of a graphGis the least number of colours needed in an edge colouring which is not preserved by any non-trivial automorphism. Broere and Pil?niak conjectured that if every non-trivial automorphism of a countable graphGmoves infinitely many edges, thenD′(G)≤2. We prove this conjecture.]]>
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机译：<！[cdata [ Abstract 区分索引 d < MML：MO>' （ g ） 图 g 是边缘所需的颜色最少数量任何非琐碎的万态态不保留的着色。 Broere和Pil？NIAK猜测，如果每个可数图 g 斜体>无数的边缘移动，那么 d '' （ G ） ≤ 2 < / mml：mn> 。我们证明了这个猜想。 ]]>
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