Semisymmetric cubic graphs as regular covers of K 3,3 |
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| Authors: | Chang Qun Wang Tie Sheng Chen |
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| Affiliation: | (1) Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, P. R. China |
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| Abstract: | A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G ≤ AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if AutX acts regularly on its arc-set. In this paper, we give the sufficient and necessary conditions for the existence of one-regular or semisymmetric Z n -covers of K 3,3. Also, an infinite family of semisymmetric Z n × Z n -covers of K 3,3 are constructed. Supported in part by NSF of China (Project No. 10571013) and by NSF of He’nan Province of China |
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| Keywords: | semisymmetric graph symmetric graph covering graph one-regular graph |
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