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Conder, Marston D.E.
Journal of algebra, 03/2021, Letnik: 569Journal Article
It is known that arc-transitive group actions on finite cubic (3-valent) graphs fall into seven classes, denoted by 1, 21, 22, 3, 41, 42 and 5, where k, k1 or k2 indicates that the action is k-arc-regular, with k2 indicating that there is no arc-reversing automorphism of order 2 (for k=2 or 4). These classes can be further subdivided into 17 sub-classes, according to the types of arc-transitive subgroups of the full automorphism group of the graph, sometimes called the ‘action type’ of the graph. In this paper, we complete the determination of the smallest graphs in each of these 17 classes (begun by Conder and Nedela in (2009) 7).
