Edge-Transitive Regular Metacyclic Covers of the Petersen Graph

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• 作者：Jiangmin Pan ; Zhaohong Huang
• 关键词：Regular cover ; Metacyclic group ; Normal quotient graph
• 刊名：Graphs and Combinatorics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：32
• 期：2
• 页码：777-784
• 全文大小：400 KB
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• 作者单位：Jiangmin Pan (1) (2)
  Zhaohong Huang (2)
  
  1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, People’s Republic of China
  2. School of Mathematics and Statistics, Yunnan University, Kunming, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Engineering Design
  
• 出版者：Springer Japan
• ISSN：1435-5914

文摘

In this paper, a complete classification is given of all the regular metacyclic covers of the Petersen graph, whose fibre-preserving groups act edge-transitively. Moreover, as an application, it is proved that there is no cubic 1-arc-regular graph with order 5m where m is a cube-free integer and coprime to 15.