The distinguishing index of connected graphs without pendant edges

Wilfried Imrich, Rafał Kalinowski, Monika Pilśniak, Mariusz Woźniak
2020 Ars Mathematica Contemporanea  
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) ≤ ∆ for every countable, connected graph G with finite maximum degree ∆ except for three small cycles. We prove that D (G) ≤ √ ∆ + 1 if additionally G does not have pendant edges.
doi:10.26493/1855-3974.1852.4f7 fatcat:hock5nu5jrc3ndgqyxijzjpbd4