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math.CO2025
On cubic vertex-transitive graphs of given girth
Ted Dobson, Ademir Hujdurović, 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.…
math.CO2025
Distinguishing finite and infinite trees of arbitrary cardinality
Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2
Let be a finite or infinite graph and the minimum number of vertices moved by the non-identity automorphisms of . We are interested in bounds on the supremum o…
math.CO2024
Monoid algebras and graph products
Wilfried Imrich, Igor Klep, Daniel Smertnig
In this note, we extend results about unique roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product…