The optimal general upper bound for the distinguishing index of infinite graphs
Monika Pilśniak, Marcin Stawiski · Journal of Graph Theory · 2019
Abstract The distinguishing index of a graph is the least cardinal number such that has an edge‐coloring with colors, which is preserved only by the trivial automorphism. We prove a general upper bound for any connected infinite graph with finite maximum degree . This is in contrast with finite graphs since for every there exist infinitely many connected, finite graphs with . We also give examples showing that this bound is sharp for any maximum degree .