| One-regular Normal Cayley Graphs on Dihedral Groups of Valency 4 or 6 with Cyclic Vertex Stabilizer |
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| 作者姓名： | Jin Ho KWAK Ju Mok OH |
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| 作者单位： | Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea |
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| 基金项目： | Supported by Com^2MaC-K0SEF. |
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| 摘 要： | A graph G is one-regular if its automorphism group Aut（G） acts transitively and semiregularly on the arc set. A Cayley graph Cay（Г, S） is normal if Г is a normal subgroup of the full automorphism group of Cay（Г, S）. Xu, M. Y., Xu, J. （Southeast Asian Bulletin of Math., 25, 355-363 （2001）） classified one-regular Cayley graphs of valency at most 4 on finite abelian groups. Marusic, D., Pisanski, T. （Croat. Chemica Acta, 73, 969-981 （2000）） classified cubic one-regular Cayley graphs on a dihedral group, and all of such graphs turn out to be normal. In this paper, we classify the 4-valent one-regular normal Cayley graphs G on a dihedral group whose vertex stabilizers in Aut（G） are cyclic. A classification of the same kind of graphs of valency 6 is also discussed.
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| 关 键 词： | Cayley图 双平面图 半及物图 数学分析 图论 |
| 收稿时间： | 2003-11-13 |
| 修稿时间： | 2003-11-132005-04-30 |
One–regular Normal Cayley Graphs on Dihedral Groups of Valency
4 or 6 with Cyclic Vertex Stabilizer |
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| Jin Ho KWAK Ju Mok OH.One-regular Normal Cayley Graphs on Dihedral Groups of Valency 4 or 6 with Cyclic Vertex Stabilizer[J].Acta Mathematica Sinica,2006,22(5):1305-1320. |
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| Authors: | Jin Ho Kwak Ju Mok Oh |
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| Institution: | (1) Mathematics, Pohang University of Science and Technology, Pohang, 790–784, Korea |
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| Abstract: | A graph G is one–regular if its automorphism group Aut(G) acts transitively and semiregularly
on the arc set. A Cayley graph Cay(Γ, S) is normal if Γ is a normal subgroup of the full
automorphism group of Cay(Γ, S). Xu, M. Y., Xu, J. (Southeast Asian Bulletin of Math., 25, 355–363
(2001)) classified one–regular Cayley graphs of valency at most 4 on finite abelian groups. Marušič, D.,
Pisanski, T. (Croat. Chemica Acta, 73, 969–981 (2000)) classified cubic one–regular Cayley graphs on
a dihedral group, and all of such graphs turn out to be normal. In this paper, we classify the 4–valent
one–regular normal Cayley graphs G on a dihedral group whose vertex stabilizers in Aut(G) are cyclic.
A classification of the same kind of graphs of valency 6 is also discussed.
Supported by Com2MaC–KOSEF |
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| Keywords: | one-regular graph Cayley graph dihedral group half-transitive graph |
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