Bounds for the average genus of the vertex-amalgamation of graphs Original Research Article

The average orientable genus of graphs has been the subject of a considerable number of recent investigations. It is the purpose of this article to examine the extent to which the average genus of the amalgamation of graphs fails to be additive over its constituent subgraphs. This discrepancy is bounded and the sharpness of these bounds discussed and compared to similar bounds for the minimum and the maximum genera of the amalgamation of graphs. The main result relies on permutation-partition pairs for its proof.