4 papers
Distinguishing adjacent vertices by ordering edges
Aleksandra Gorzkowska, Jakub Kwaśny
The 1-2-3 Conjecture states that for every graph without isolated edges, there exists an edge-weighting from such that adjacent vertices receive distinct sums of weight…
Arc-distinguishing of orientations of graphs
Aleksandra Gorzkowska, Jakub Kwaśny
The distinguishing index of a graph is the minimum number of colours in an edge colouring preserved only by the identity automorphism. We study how orienting the edges…
Breaking small automorphisms by list colourings
Jakub Kwaśny, Marcin Stawiski
For a graph G, we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of G that break every small automorphism of G. We…
List distinguishing index of graphs
Jakub Kwaśny, Marcin Stawiski
We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-ide…