The distinguishing number D (G) of a graph is the least integer d such that there is ad‐
labeling of the vertices of G that is not preserved by any nontrivial automorphism of G. We …

Suppose Γ is a group acting on a set X. A k-labeling of X is a mapping c: X→{1, 2,…, k}. A
labeling c of X is distinguishing (with respect to the action of Γ) if for any g∈ Γ, g≠ idX, there …

The distinguishing number D (G) of a graph G is the least integer d such that G has a
labeling with d labels that is preserved only by a trivial automorphism. We prove that …

This work introduces the technique of using a carefully chosen determining set to prove the
existence of a distinguishing labeling using few labels. A graph $ G $ is said to be $ d …

The distinguishing number of a group $ A $ acting faithfully on a set $ X $, denoted $ D (A,
X) $, is the least number of colors needed to color the elements of $ X $ so that no …

Let $ G $ be a graph. A vertex labeling of $ G $ is distinguishing if the only label-preserving
automorphism of $ G $ is the identity map. The distinguishing number of $ G $, $ D (G) $, is …

The distinguishing number of a graph G, denoted D (G), is the minimum number of colors
such that there exists a coloring of the vertices of G where no nontrivial graph automorphism …

Let G be a group acting faithfully on a set X. The distinguishing number of the action of G on
X is the smallest number of colors such that there exists a coloring of X where no nontrivial …

We study the base sizes of finite quasiprimitive permutation groups of twisted wreath type,
which are precisely the finite permutation groups with a unique minimal normal subgroup …

The distinguishing chromatic number _D(G) of a graph G is the least integer k such that
there is a proper k-coloring of G which is not preserved by any nontrivial automorphism of G …