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Distinguishing vertices of a graph: automorphisms and palettes

Banff International Research Station for Mathematical Innovation and Discovery

If we want to distinguish all vertices of the graph by coloring its elements, then we have the following possibilities. We can use the concept of coloring that breaks non-trivial automorphisms, or coloring that induces different color palettes for each vertex. These approaches are not independent. Always distinguishing using automorphisms is stronger than using palettes. And, very often, the corresponding parameters are quite distant from each other. We will show several situations when the corresponding parameters are close to each other. The talk is based on the papers [1] and [2]. [1] R. Kalinowski, M. PilŠniak, J. PrzybyŠo and M. Woźniak, How to personalize the vertices of a graph, European Journal of Combinatorics 40 (2014), 116-123. [2] R. Kalinowski, M. PilŠniak, M. Woźniak, Distinguishing graphs by total colourings, Ars Mathematica Contemporanea 11 (2016), 79-89.

Mathematics; Combinatorics; Group theory and generalizations; Discrete mathematics

video/mp4

Author affiliation: AGH University of Science and Technology

2019-03-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68826

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/