The Distinguishing Index of Infinite Graphs
نویسندگان
چکیده
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 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 D′(G) 6 ∆(G) for an arbitrary infinite graph. Nonetheless, the distinguishing 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.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015