# Infinite cubic vertex-transitive graphs

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R\" ognvaldur G. M\" oller

University of Iceland

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**Minisymposium:**
STRUCTURE AND PROPERTIES OF VERTEX-TRANSITIVE GRAPHS

**Content:**
Tutte's two papers from 1947 and 1959 on cubic graphs were the starting point of the in-depth study of the interplay between the structure of a group and the structure of a graph that the group acts on. In this talk I will describe applications of Tutte's ideas where it is assumed that the graph is infinite and the stabilizers of vertices are infinite.