12 papers
Asymmetric edge-coloring of graphs with simple automorphism group
Mariusz Grech, Andrzej Kisielewicz
The distinguishing index of a graph is the least number such that has an edge-coloring with colors preserved only by the trivial automorphism. In this paper…
A class of graphs with distinguishing index
Mariusz Grech, Andrzej Kisielewicz
An edge-coloring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Lehner, Pilśniak, and Stawiski proved that all connected regular graph…
Distinguishing actions of symmetric groups and related graphs
Mariusz Grech, Andrzej Kisielewicz
The distinguishing number of an action of a group on a set is the least size of a partition of such that no element of acting nontrivially on preserves…
Distinguishing simple groups
Mariusz Grech, Andrzej Kisielewicz
The distinguishing number of a graph is the least size of a partition of the vertices of such that no non-trivial automorphism of preserves this partition. We sh…
Abelian permutation groups with graphical representations
Mariusz Grech, Andrzej Kisielewicz
In this paper we characterize permutation groups that are automorphism groups of coloured graphs and digraphs and are abelian as abstract groups. This is done in terms of basic per…
Wreath product in automorphism groups of graphs
Mariusz Grech, Andrzej Kisielewicz
The automorphism group of the composition of graphs contains the wreath product of the automorphism groups of the corresponding graphs. The classica…