Graph genus

In topological graph theory, an embedding (also spelled imbedding) of a graph ${\displaystyle G}$ on a surface ${\displaystyle \Sigma }$ is a representation of ${\displaystyle G}$ on ${\displaystyle \Sigma }$ in which points of ${\displaystyle \Sigma }$ are associated with vertices and simple arcs (homeomorphic images of ${\displaystyle [0,1]}$) are associated with edges in such a way that:

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