Abstract
There are many results on the flexibility of (general) embeddings of graphs, but few are known about that of strong embeddings. In this paper, we study the flexibility of strong embeddings of circular and Mobius ladders on the projective plane and the Klein bottle by using the joint tree model of embeddings. The numbers of (nonequivalent) general embeddings and strong embeddings of circular and Mobius ladders on these two nonorientable surfaces are obtained, respectively. And the structures of those strong embeddings are described.
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