Wilfried Imrich

collaborators

4 papers

math.CO2025

On cubic vertex-transitive graphs of given girth

Ted Dobson, Ademir HujduroviÄ, Wilfried Imrich +1

A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost.…

cs.DM2025

Local Search Improvements for Soft Happy Colouring

Mohammad Hadi Shekarriz, Dhananjay Thiruvady, Asef Nazari +1

For $0 \leq I ¨ \leq 1$ and a coloured graph $G$ , a vertex $v$ is $I ¨ $ -happy if at least $I ¨ deg (v)$ of its neighbours have the same colour as $v$ . Soft happy colouring of a p…

math.CO2025

Distinguishing finite and infinite trees of arbitrary cardinality

Wilfried Imrich, RafaÅ 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 $I^ (G)$ …

math.CO2025

Monoid algebras and graph products

Wilfried Imrich, Igor Klep, Daniel Smertnig

In this note, we extend results about unique $n^{th}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product…