Abstract
A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. Let p be a prime. By Folkman [J. Combin. Theory 3 (1967), 215–232], there is no cubic semisymmetric graph of order 2p or 2p2, and by Hua et al. [Science in China A 54 (2011), 1937–1949], there is no cubic semisymmetric graph of order 4p2. Lu et al. [Science in China A 47 (2004), 11–17] classified connected cubic semisymmetric graphs of order 6p2. In this paper, for p > q ≥ 5 two distinct odd primes, it is shown that the sufficient and necessary conditions which a connected cubic edge transitive bipartite graph of order 2qp2 is semisymmetric.
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Supported by the National Natural Science Foundation of China (Nos. 11301159, 11671030, 11601132, 11501176), the Education Department of Henan Science and Technology Research Key Project (No. 13A110543).
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Hua, Xh., Guo, St. & Chen, L. Cubic Semisymmetric Graphs of Order 2qp2. Acta Math. Appl. Sin. Engl. Ser. 35, 629–637 (2019). https://doi.org/10.1007/s10255-019-0839-1
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DOI: https://doi.org/10.1007/s10255-019-0839-1