Geodesic
The distinguishing index of connected graphs without pendant edges
Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 117-126.

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We consider edge colourings, not necessarily proper. The distinguishing index D′(G) of a graph G is the least number of colours in an edge colouring that is preserved only by the identity automorphism. It is known that D′(G) ≤ Δ for every countable, connected graph G with finite maximum degree Δ except for three small cycles. We prove that D′(G) ≤ ⌈√Δ⌉ + 1 if additionally G does not have pendant edges.
DOI : 10.26493/1855-3974.1852.4f7
Keywords: Symmetry breaking, distinguishing index of a graph 
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Wilfried Imrich; Rafał Kalinowski; Monika Pilśniak; Mariusz Woźniak. The distinguishing index of connected graphs without pendant edges. Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 117-126. doi : 10.26493/1855-3974.1852.4f7. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1852.4f7/

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