Arc-transitive regular cyclic covers of the complete bipartite graph \(\mathsf{K}_{p,p}\)

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• 作者：Jiangmin Pan ; Zhaohong Huang ; Zhe Liu
• 关键词：Arc ; transitive graph ; Regular cover ; Complete bipartite graph ; Cayley graph ; 20B15 ; 20B30 ; 05C25
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：42
• 期：2
• 页码：619-633
• 全文大小：486 KB
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• 作者单位：Jiangmin Pan (1)
  Zhaohong Huang (2)
  Zhe Liu (3)
  
  1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, People鈥檚 Republic of China
  2. School of Mathematics and Statistics, Yunnan University, Kunming, People鈥檚 Republic of China
  3. College of Science, Zhejiang University of Agriculture and Forestry, Hangzhou, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Convex and Discrete Geometry
  Order, Lattices and Ordered Algebraic Structures
  Computer Science, general
  Group Theory and Generalizations
  
• 出版者：Springer U.S.
• ISSN：1572-9192

文摘

Characterizing regular covers of edge-transitive or arc-transitive graphs is currently a hot topic in algebraic graph theory. In this paper, we will classify arc-transitive regular cyclic covers of the complete bipartite graph \(\mathsf{K}_{p,p}\) for each odd prime \(p\). The classification consists of four infinite families of graphs. In particular, such covers exist for each odd prime \(p\). The regular elementary abelian covers of \(\mathsf{K}_{p,p}\) are considered in a sequel.