On pentavalent 1-transitive Cayley graphs

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• 作者：Bo Ling^a ; ^{bolinggxu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ben Gong Lou^a ; ^{bengong188@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jing Jian Li^a ; ^b ; ^{lijjhx@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：1-transitive ; Cayley graph ; Core-free ; Normal quotient
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 April 2016
• 年：2016
• 卷：339
• 期：4
• 页码：1335-1343
• 全文大小：395 K

文摘

A Cayley graph mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15004276&_mathId=si36.gif&_user=111111111&_pii=S0012365X15004276&_rdoc=1&_issn=0012365X&md5=7f79336cf097f258cb384476e88c5ca3">mage" height="15" width="98" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0012365X15004276-si36.gif">mathContainer hidden">mathCode"><math altimg="si36.gif" overflow="scroll">Γ=mathvariant="sans-serif">Cay(G,S)math> is said to be core-free if mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15004276&_mathId=si4.gif&_user=111111111&_pii=S0012365X15004276&_rdoc=1&_issn=0012365X&md5=aaf84101402bee831ffb5e13b5578a1e" title="Click to view the MathML source">GmathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">Gmath> is core-free in some mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15004276&_mathId=si38.gif&_user=111111111&_pii=S0012365X15004276&_rdoc=1&_issn=0012365X&md5=2a52cd13f53b11e24b8b5d942cdcea43">mage" height="13" width="70" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0012365X15004276-si38.gif">mathContainer hidden">mathCode"><math altimg="si38.gif" overflow="scroll">X≤mathvariant="sans-serif">AutΓmath>. In this paper, a characterization of connected core-free pentavalent 1-transitive Cayley graphs is given. Moreover, the argument in this paper also gives another proof for a result in Zhou and Feng (2010) which says that all connected pentavalent 1-transitive Cayley graphs of finite non-abelian simple groups are normal.