We introduce the distinguishing index D′(G) of a graph G as the least number d such that G
has an edge-colouring with d colours that is only preserved by the trivial automorphism. This …

A vertex coloring of a graph GG is called distinguishing if no nonidentity automorphisms of
GG can preserve it. The distinguishing number of GG, denoted by D (G) D(G), is the …

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 …

The distinguishing index $ D^\prime (G) $ of a graph $ G $ is the least cardinal $ d $ such
that $ G $ has an edge colouring with $ d $ colours that is only preserved by the trivial …

We introduce the total distinguishing number D (G) of a graph G as the least number d such
that G has a total colouring (not necessarily proper) with d colours that is only preserved by …

The\textit {Distinguishing Chromatic Number} of a graph $ G $, denoted $\chi_D (G) $, was
first defined in\cite {collins} as the minimum number of colors needed to properly color $ G …

A coloring is distinguishing (or symmetry breaking) if no non-identity automorphism
preserves it. The distinguishing threshold of a graph $ G $, denoted by $\theta (G) $, is the …

A graph G is said to be k-distinguishable if every vertex of the graph can be colored from a
set of k colors such that no non-trivial automorphism fixes every color class. The …

A distinguishing coloring of a simple graph $ G $ is a vertex coloring of $ G $ which is
preserved only by the identity automorphism of $ G $. In other words, this …

Dans cette thèse nous étudions trois jeux à objectif compétitif sur les graphes. Les jeux à
objectif compétitif proposent une approche dynamique des problèmes d'optimisation …