Geodesic
Nordhaus-Gaddum type inequalities for the distinguishing index
Ars Mathematica Contemporanea, Tome 20 (2021) no. 2, pp. 223-231.

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The distinguishing index of a graph G, denoted by D′(G), is the least number of colours in an edge colouring of G not preserved by any nontrivial automorphism. This invariant is defined for any graph without K2 as a connected component and without two isolated vertices, and such a graph is called admissible. We prove the Nordhaus-Gaddum type relation:2 ≤ D′(G) + D′(Ḡ) ≤ Δ(G) + 2for every admissible connected graph G of order |G| ≥ 7 such that Ḡ is also admissible.
DOI : 10.26493/1855-3974.2173.71a
Keywords: Symmetry breaking in graphs, distinguishing index, Nordhaus-Gaddum type bounds 
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Monika Pilśniak. Nordhaus-Gaddum type inequalities for the distinguishing index. Ars Mathematica Contemporanea, Tome 20 (2021) no. 2, pp. 223-231. doi : 10.26493/1855-3974.2173.71a. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2173.71a/

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