CONSTRUCTION OF GRAPHS WHICH ARE NOT UNIQUELY AND NOT FAITHFULLY EMBEDDABLE IN SURFACES
Seiya Negami · Institutional Repositories DataBase (IRDB) · 1985
A graph ＄G＄ is said to be uniquely embeddable in a surface ＄F^{2}＄ if for any two embeddings ＄f_{1},f_{2}＄ : ＄G￥rightarrow F^{2}＄, there is an automorphism ＄￥sigma＄ : ＄G￥rightarrow G＄ and a homeomorphism ＄h;F^{2}￥rightarrow F^{2}＄ such that ＄ h_{￥circ}f_{1}=f_{2}￥circ￥sigma＄ . A graph ＄G＄ is said to be faithfully embeddable in a surface ＄F^{2}＄ if ＄G＄ admits an embedding ＄f:G￥rightarrow F^{2}＄ such that for any automorphism ＄￥sigma:G￥rightarrow G＄ , there is a homeomorphism ＄h＄ ; ＄F^{2}￥rightarrow F^{2}＄ with ＄ h_{0}f=f￥circ￥sigma＄ . Given a hyperbolic closed surface ＄F^{2}＄, an infinite number of 6-connected graphs which are not uniquely or not faithfully embeddable in ＄F^{2}＄ will be constructed systematically.