AbstractA graphGis called the 2‐amalgamationof subgraphsG1andG2ifG=G1∪G2andG1∩G2= {x, y}, 2 distinct points. in this case we writeG=G1∪{x, y}G2. in this paper we show that the orientable genus, γ(G), satisfies the inequalities γ(G1) + γ(G2) − 1 ≤ γ(G1∪{x, y}G2) ≤ γ(G1) + γ(G2) + 1 and that this is the best possible result, i. e., the resulting three values for γ(G1∪{x, y}G2) which are possible can actually be realized by approp