# Marston Conder: The smallest symmetric cubic graphs with given type

Source: Discrete mathematics seminar

**Povezava do seminarja/link to the seminar:**

Topic: Slovenia Discrete Maths Seminar

Time: 10:15 Tuesday 5 May 2020 (Slovenia time)

Join Zoom Meeting https://auckland.zoom.us/j/91393129821

**The smallest symmetric cubic graphs with given type**

**Marston Conder** (University of Auckland, New Zealand)

**Abstract. **It is known that arc-transitive group actions on finite cubic (3-valent) graphs fall into seven classes, denoted by 1, 2^1, 2^2, 3, 4^1, 4^2 and 5, where s, s^1 or s^2 indicates that the action is s-arc-regular, and with s^2 indicating that there is no arc-reversing automorphism of order 2 for s = 2 or 4). These classes can be further subdivided into17 sub-classes, according to the types of arc-transitive subgroups of the full automorphism group f the graph, sometimes called the `action type' of the graph.

In this talk, I'll describe some recent work that completes the determination f the smallest graphs in each of these 17 classes (begun 12 years ago).