Rafał Kalinowski

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math.CO2025

Distinguishing finite and infinite trees of arbitrary cardinality

Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2

Let $G$ be a finite or infinite graph and $m (G)$ the minimum number of vertices moved by the non-identity automorphisms of $G$ . We are interested in bounds on the supremum $Δ (G)$ o…

math.CO2025

Distinguishing symmetric digraphs by proper arc-colourings of type I

Rafał Kalinowski, Monika Pilśniak, Magdalena Prorok

A symmetric digraph $G$ is obtained from a simple graph $G$ by replacing each edge $uv$ with a pair of opposite arcs $uv$ , $v u$ . An arc-…

math.CO2023

Asymmetrizing infinite trees

Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2

A graph $G$ is asymmetrizable if it has a set of vertices whose setwise stablizer only consists of the identity automorphism. The motion $m$ of a graph is the minimum number of ver…