Flexibility of Circular Graphs $C(2n,2)$ on the Projective Plane

Abstract

In this paper, we study the flexibility of embeddings of circular graphs $C(2n,2)$, $n\ge 3$ on the projective plane. The numbers of (non-equivalent) embeddings of $C(2n,2)$ on the projective plane are obtained, and by describing structures of these embeddings, the numbers of (non-equivalent) weak embeddings and strong embeddings of $C(2n,2)$ on the projective plane are also obtained.