Abstract

AbstractA graph G is called the 2‐amalgamation of subgraphs G1 and G2 if G = G1 ∪ G2 and G1 ∩ G2 = {x, y}, 2 distinct points. in this case we write G = 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 appropriate choices for G1 and G2.

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