100p阶五度对称图（英文）Pentavalent Symmetric Graphs of Order 100p
吴马威,徐尚进,谢金华
摘要(Abstract)：
如果一个图的自同构群作用在它的弧集上是传递的,则称这个图为对称图.该文研究全自同构群无可解极小正规子群的100p阶连通五度对称图.结果表明,这样的图是不存在的.
关键词(KeyWords)： 对称图;可解极小正规子群;非交换单群
基金项目(Foundation): The Project Supported by the National Natural Science Foundation of China(Grant 10961004,11361006,11461004);; Guangxi Science Foundation(proj.no.2015GXNSFAA139001)
作者(Author): 吴马威,徐尚进,谢金华
DOI: 10.16601/j.cnki.issn1001-8743.2018.01.001
参考文献(References)：
- [1]CONDER M D E,DOBCSNYI P.Trivalent symmetric graphs on up to 768vertices[J].J Combin Math Combin Comput,2002,40:41-63.
- [2]FENG Y Q,KWAK J H.Cubic symmetric graphs of order twice an odd prime power[J].J Aust Math Soc,2006,81:153-164.
- [3]FENG Y Q,KWAK J H.Classifying cubic symmetric graphs of order 10pand 10p2[J].Sci China(A),2006,49:300-319.
- [4]FENG Y Q,KWAK J H.Cubic s-regular graphs of order 2p3[J].J Graph Theory,2006,52:341-352.
- [5]FENG Y Q,KWAK J H.Cubic symmetric graphs of order asmall number times aprime or aprime square[J].JCombin Theory(B),2007,97:627-646.
- [6]FENG Y Q,KWAK J H,WANG K S.Classifying cubic symmetric graphs of order 8por 8p2[J].Europ J Combin,2005,26:1033-1052.
- [7]LI Y T,FENG Y Q.Pentavalent one-regular graphs of square-free order[J].AlgebraColloquium,2010,17:515-524.
- [8]HUA X H,FENG Y Q.Pentavalent symmetric graphs of order 8p[J].J Beijing Jiaotong University,2011,35:132-135.
- [9]HUA X H,FENG Y Q,LEE J.Pentavalent symmetric graphs of order 2pq[J].Discrete Math,2011,311:2259-2267.
- [10]YANG D W,FENG Y Q,DU J L.Pentavalent symmetric graphs of order 2pqr[J].Discrete Math,2016,339:522-532.
- [11]GUO S T,ZHOU J X,FENG Y Q.Pentavalent symmetric graphs of order 12p[J].Electronic J Combin,2011,18:1-13.
- [12]LING B.Classifying pentavalnet symmetric graphs of order 24p[J].Bulletin of the Iranian Mathematical Society,2017,43:1855-1866.
- [13]SABIDUSSI B O.Vertex-transitive graphs[J].Monash Math,1964,68:426-438.
- [14]HUPPERT B.Eudiche gruppen I[M].Berlin:Springer-Verlag,1967.
- [15]ROBINSON D J.A Course in the theory of groups[M].New York:Springer-Verlag,1982.
- [16]CONWAY J H,CURTIS R T,NORTON S P,et al.Atlas of finte groups[M].Oxford:Clarendon Press,1985.
- [17]LORIMER P.Vertex-transitive graphs:Symmetric graphs of prime valency[J].J Graph Theory,1984,8:55-68.
- [18]GUO S T,FENG Y Q.A note on pentavalent s-transitive graphs[J].Discrete Math,2012,312:2214-2216.
- [19]ZHOU J X,FENG Y Q.On symmetric graphs of valency five[J].Discrete Math,2010,310:1725-1732.
- [20]DU J L,FENG Y Q,ZHOU J X.Pentavalent symmetric graphs admitting vertex-transitive non-abelian simple groups[J].Europ J Combin,2017,63:134-145.
- [21]GAP.Groups,algorithms and programming[CP/OL].[2017-03-16].http://www.gap-system.org.