摘要
Two cellular embeddings i ： G→S and j ： G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h ： S → S such that hi = j. The genus polynomial of a graph G is defined by g[G]（x）=∞∑g=0agx^g, where ag is the number of equivalence classes of embeddings of G into the orientable surface Sg with g genera. In this paper, we compute the genus polynomial of a graph obtained from a cycle by replacing each edge by two multiple edges.
Two cellular embeddings i ： G→S and j ： G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h ： S → S such that hi = j. The genus polynomial of a graph G is defined by g[G]（x）=∞∑g=0agx^g, where ag is the number of equivalence classes of embeddings of G into the orientable surface Sg with g genera. In this paper, we compute the genus polynomial of a graph obtained from a cycle by replacing each edge by two multiple edges.
