Activity: Talk or presentation › Invited talk › Science to science
Automata and graphs are associated in many ways. For invertible automata one can define the automaton group and observe its action on the set of finite words over the input alphabet. This leads to the construction of Schreier graphs. The sum of all distances in a graph, called Wiener index, is a graph property of wide interest. Harry Wiener showed that the properties of molecules are related to the Wiener index of chemical structural formulas. In my talk I will give a basic introduction to automata theory, Schreier graphs and the Wiener index. I will show some examples of automata and their properties, in particular the behaviour of the Wiener index on their corresponding Schreier graphs.