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Grannell, M. J.; Griggs, T. S. and Knor, M.
(2003).
in an orientable surface.
Abstract
An embedding of a graph
is said to be regular if and only if for every two triples
and
, where
is an edge incident with the vertex
and the face
, there exists an automorphism of
which maps
to
,
to
and
to
. We show that for
(mod 8) there is, up to isomorphism, precisely one regular Hamiltonian embedding of
in an orientable surface, and that for
(mod 8) there are precisely two such embeddings. We give explicit constructions for these embeddings as lifts of spherical embeddings of dipoles.