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| Tetravalent Edge-transitive Cayley Graphs of PGL （2, p） | |
| 作者姓名： | Xiao-hui HUA Shang-jin XU Yun-ping DENG |
| 作者单位： | [1]College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China [2]School of Mathematics and Information Science, Guangxi University, Nanning 530004, China [3]Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
| 基金项目： | Supported by the National Natural Science Foundation of China （No.11171020,10961004）, the Henan Province Foundation and Frontier Technology Research Plan （No.112300410205）, the Education Department of Henan Science and Technology Research Key Project （No.13A110543）, and the Doctoral Fundamental Research Fund of Hennan Normal University （11102）. |
| 摘 要： | t Let F = Cay（G, S）, R（G） be the right regular representation of G. The graph Г is called normal with respect to G, if R（G） is normal in the full automorphism group Aut（F） of F. Г is called a bi-normal with respect to G if R（G） is not normal in Aut（Г）, but R（G） contains a subgroup of index 2 which is normal in Aut（F）. In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL（2,p） are either normal or bi-normal when p ≠ 11 is a prime. |
| 关 键 词： | Cayley图 PGL 边传递 四价 全自同构群 正则表示 素数 |
Tetravalent edge-transitive cayley graphs of PGL (2, p) |
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| Xiao-hui HUA,Shang-jin XU,Yun-ping DENG.Tetravalent edge-transitive cayley graphs of PGL (2, p)[J].Acta Mathematicae Applicatae Sinica,2013,29(4):837-842. | |
| Authors: | Xiao-hui Hua Shang-jin Xu Yun-ping Deng |
| Institution: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China 2. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, China 3. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China |
| Abstract: | Let Γ = Cay(G, S), R(G) be the right regular representation of G. The graph Γ is called normal with respect to G, if R(G) is normal in the full automorphism group Aut(Γ) of Γ. Γ is called a bi-normal with respect to G if R(G) is not normal in Aut(Γ), but R(G) contains a subgroup of index 2 which is normal in Aut(Γ). In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL(2, p) are either normal or bi-normal when p ≠ 11 is a prime. |
| Keywords: | Cayley graph normal bi-normal simple group |
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