Arc-transitive abelian regular covering graphs. (English) Zbl 1353.05128
Author’s abstract: A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by M. D. E. Conder and J. Ma [J. Algebra 387, 215–242 (2013; Zbl 1283.05123)], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder-Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph \(K_5\) which can be obtained by lifting the arc-transitive subgroups of automorphisms \(A_5\) and AGL(1,5) are classified.
Reviewer: Ioan Tomescu (Bucureşti)
MSC:
05E18 | Group actions on combinatorial structures |
05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
Keywords:
arc-transitive graph; regular cover; abelian cover; symmetric cover; 4-valent symmetric graphCitations:
Zbl 1283.05123Software:
MagmaReferences:
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