3 citations · 4 across the 11 of their papers we have counts for
13 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…
Symmetry groups of boolean functions: simple groups
Mariusz Grech, Andrzej Kisielewicz
We consider the problem of characterizing the class of those permutation groups that are the symmetry groups of Boolean functions. These are exactly the automorphism groups of hype…
Subgroups of simple primitive permutation groups defined by unordered relations (Automorphism groups of hypergraphs)
Mariusz Grech, Andrzej Kisielewicz
The problem of describing the invariance groups of unordered relations, called briefly \emph{relation groups}, goes back to classical work by H. Wielandt. In general, the problem t…
Decompositions of the authomorphism groups of edge-colored graphs into the direct product of permutation groups
Mariusz Grech
In the paper Graphical complexity of products of permutation groups, M. Grech, A. Jez, A. Kisielewicz have proved that the direct product of automorphism groups of edge-colored gra…
Symmetry groups of Boolean Functions
Mariusz Grech, Andrzej Kisielewicz
We prove that every abelian permutation group, but known exceptions, is the symmetry group of a boolean function. This solves the problem posed in the book by Clote and Kranakis. I…
Graphical Cyclic Permutation Groups
Mariusz Grech
We establish conditions for a permutation group generated by a single permutation of a prime power order to be an automorphism group of a graph or an edge-colored graph. This corre…
The Cerny conjecture for automata respecting intervals of a directed graph
M. Grech, A. Kisielewicz
The Černý's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n-11)^2. We prove this conjecture for a class…
All totally symmetric colored graphs
Mariusz Grech, Andrzej Kisielewicz
In this paper we describe all edge-colored graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. They correspond to fully s…