Geodesic
Improving upper bounds for the distinguishing index
Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 259-274.

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The distinguishing index of a graph G, denoted by Dʹ(G), is the least number of colours in an edge colouring of G not preserved by any non-trivial automorphism. We characterize all connected graphs G with Dʹ(G) ≥ Δ (G). We show that Dʹ(G) ≤ 2 if G is a traceable graph of order at least seven, and Dʹ(G) ≤ 3 if G is either claw-free or 3-connected and planar. We also investigate the Nordhaus-Gaddum type relation: 2 ≤ Dʹ(G) + Dʹ(‾G) ≤ max{Δ (G), Δ (‾G)} + 2 and we confirm it for some classes of graphs.
DOI : 10.26493/1855-3974.981.ff0
Keywords: Edge colouring, symmetry breaking in graph, distinguishing index, claw-free graph, planar graph 
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Monika Pilśniak. Improving upper bounds for the distinguishing index. Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 259-274. doi : 10.26493/1855-3974.981.ff0. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.981.ff0/

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