2022/07/29 by Jakub Kwaśny, Kwaśny, Jakub, Marcin Stawiski +1
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2207.14728
An edge colouring of a graph is called distinguishing if there is no non-trivial automorphism which preserves it. We prove that every at most countable, finite or infinite, connected regular graph of order at least 7 admits a distinguishing edge colouring from any set of lists of length 2. Furthermore, we show that the same holds for connected regular graphs of order κ where κ is a fixed point of the aleph hierarchy.