The distinguishing index D′(G) of a graph G is the least number of colours needed in an
edge colouring which is not preserved by any non-trivial automorphism. Broere and Pilśniak …

A graph G is said to be 2-distinguishable if there is a 2-labeling of its vertices which is not
preserved by any nontrivial automorphism of G. We show that every locally finte graph with …

Abstract A group AA acting faithfully on a set XX is 2 2-distinguishable if there is a 2 2-
coloring of XX that is not preserved by any nonidentity element of AA, equivalently, if there is …

Call a colouring of a graph distinguishing, if the only colour preserving automorphism is the
identity. A conjecture of Tucker states that if every automorphism of a graph $ G $ moves …

Call a colouring of a graph distinguishing if the only colour preserving automorphism is the
identity. A conjecture of Tucker states that if every automorphism of a connected graph GG …

A distinguishing colouring of a graph is a colouring of the vertex set such that no non-trivial
automorphism preserves the colouring. Tucker conjectured that if every non-trivial …

If a graph G has distinguishing number 2, then there exists a partition of its vertex set into two
parts, such that no nontrivial automorphism of G fixes setwise the two parts. Such a partition …

Given a group Γ acting on a set X, a k-coloring ϕ: X→{1,…, k} of X is distinguishing with
respect to Γ if the only γ∈ Γ that fixes ϕ is the identity action. The distinguishing number of …

Abstract Let G⩽ Sym (X) G\leqslantSym(X) be a group of permutations of a countable set X
X. Call a colouring of XX asymmetric if no g∈ G∖ id g∈G∖{id} preserves all colours. The …

A vertex colouring of a graph is called asymmetric if the only automorphism which preserves
it is the identity. Tucker conjectured that if every automorphism of a connected, locally finite …