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arXiv · 1607.02618

On cubic symmetric non-Cayley graphs with solvable automorphism groups

Yan-Quan Feng·Klavdija Kutnar·Dragan Marusic·Da-Wei Yang
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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 $2^2$, 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 $2^2$ with a solvable automorphism group is constructed. The smallest graph in this family has order 6174.

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Yan-Quan Feng, Klavdija Kutnar, Dragan Marusic, Da-Wei Yang. 2016-07-09. On cubic symmetric non-Cayley graphs with solvable automorphism groups. https://arxiv.org/abs/1607.02618

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