Venue: PovoZero - Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula seminari - Sala Seminari "-1"
At: 4 PM
Thursday 26 September 2019
Pablo Spiga, Universita degli Studi di Milano-Bicocca
How vertex-stabilizers grow?
Here we are interested in highly symmetric graphs. (All basic terminology will be given during the talk.) There are various natural ways to “measure” the degree of symmetry of a graph and, in this talk, we look at two possibilities. First, we consider graphs Γ having a group of automorphisms acting transitively on the paths of length s ≥ 1, starting at a given vertex. The larger the value of s is, the more symmetric the graph will be. However, we show that large values of s impose severe restrictions on the structure of Γ and on the size of the stabilizer of a vertex of Γ. This will lead us to the second perspective. We take the size of the stabilizer of a vertex of Γ as a measure of the transitivity. This measure is somehow unbiased among the
graphs having the same number of vertices. Again we present some results showing, in some very specific cases, that nature is not as diverse as one might expect: graphs have either rather small vertex stabilizers or they can be classified. Finally we give some applications of these investigations: to the enumeration problem of symmetric graphs and to the problem of creating a database of small symmetric graphs.
Tuesday 29 October 2019
- Giuseppe Buttazzo, Università di Pisa