On cubic symmetric non-Cayley graphs with solvable automorphism groups

2016/07/09 by Feng, Yan-Quan, Kutnar, Klavdija, Marusic, Dragan +1
#05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.02618

Abstract

It was proved in [Y.-Q. Feng, C. H. Li and J.-X. Zhou, Symmetric cubic graphs with solvable automorphism groups, \em European J. Combin. \bf 45 (2015), 1-11] that a cubic symmetric graph with a solvable automorphism group is either a Cayley graph or a 2-regular graph of type 2², that is, a graph with no automorphism of order 2 interchanging two adjacent vertices. In this paper an infinite family of non-Cayley cubic 2-regular graphs of type 2² with a solvable automorphism group is constructed. The smallest graph in this family has order 6174.

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