An additivity theorem for the genus of a graph
The generalized genus g(G) of a connected graph G is defined as \(g(G)=\min \{\gamma (G),{\tilde \gamma}(G)\}\) where \(\gamma\) (G), \({\tilde \gamma}\)(G) are the orientable and non-orientable genera of G, respectively. It is proved that if G is obtained from disjoint connected graphs \(H_ 1\) and \(H_ 2\) by identifying an edge (vertex) in \(H_ 1\) with an edge (vertex) in \(H_ 2\) then \(g(G)=g(H_ 1)+g(H_ 2)\). The proofs utilize a new combinatorial representation of embeddings.
scientific article; zbMATH DE number 4002116
scientific article