Exponential Families of Non-isomorphic Non-triangular Orientable Genus Embeddings of Complete Graphs

It is shown that for every i∈{1,2,…,11}\{3,4,7} the complete graph K12s+i for s⩾d(i)∈{1,2,3,4} has at least h(i)4s non-isomorphic orientable genus embeddings, where h(i)∈{1,12,14,18}.