Identifying vertices of a planar diagram

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Hi all,

I'm having trouble understanding what 'identifying vertices' means for a planar model of a surface. This is in the context of trying to classify a closed, connected surface to see whether it is homeomorphic to the sphere, or connected sums of tori, or connected sums of projective planes.

My text says something like 'we have two adjacent vertices in different equivalence classes'. How do I see which equivalence class the vertex belongs to? I thought only the edges of the diagram belonged to equivalence classes.

Thanks in advance.
 

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