We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we gene...We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.展开更多
In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In parti...In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are Z3,Z5or a subgroup of Z2^5.展开更多
文摘We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.
文摘In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are Z3,Z5or a subgroup of Z2^5.
