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Cubic vertex-transitive non-Cayley graphs of order 12p

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Abstract

A graph is said to be vertex-transitive non-Cayley if its full automorphism group acts transitively on its vertices and contains no subgroups acting regularly on its vertices. In this paper, a complete classification of cubic vertex-transitive non-Cayley graphs of order 12p, where p is a prime, is given. As a result, there are 11 sporadic and one infinite family of such graphs, of which the sporadic ones occur when p equals 5, 7 or 17, and the infinite family exists if and only if p ≡ 1 (mod 4), and in this family there is a unique graph for a given order.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11671030, 11171020 and 11231008) and the Fundamental Research Funds for the Central Universities (Grant No. 2015JBM110).

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Wei-Juan Zhang, Yan-Quan Feng & Jin-Xin Zhou

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  1. Wei-Juan Zhang
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  2. Yan-Quan Feng
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  3. Jin-Xin Zhou
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Correspondence to Jin-Xin Zhou.

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Zhang, WJ., Feng, YQ. & Zhou, JX. Cubic vertex-transitive non-Cayley graphs of order 12p. Sci. China Math. 61, 1153–1162 (2018). https://doi.org/10.1007/s11425-016-9095-8

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