3 problems

Let $G$ be a graph, and let $g_k(G)$ denote the number of equivalence classes of 2-cell embeddings of $G$ on the orientable surface of genus $k$. The sequence…

Let $G$ be a graph that triangulates some surface, and let its genus distribution be the sequence of numbers of $2$-cell embeddings of $G$ in orientable surfaces of each genus. Sur…

For a graph $G$ and a nonnegative integer $g$, let $a_g(G)$ denote the number of $2$-cell embeddings of $G$ in an orientable surface of genus $g$, counted up to combinatorial homeo…