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Ma, Jicheng

Arc-transitive abelian regular covering graphs. (English) Zbl 1353.05128

Int. J. Algebra Comput. 26, No. 7, 1369-1393 (2016).
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)

Cited in 2 Documents

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 graph

Citations:

Zbl 1283.05123

Software:

Magma
Cite Review PDF
Full Text: DOI

References:

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