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 ...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.展开更多
Calculating the genus distributions of ladder graphs is a concerned topic in topological graph theory.In this paper,we formulate several ladder-class graphs by using a starting graph iterative amalgamation with copies...Calculating the genus distributions of ladder graphs is a concerned topic in topological graph theory.In this paper,we formulate several ladder-class graphs by using a starting graph iterative amalgamation with copies of a path to construct a base graph and then adding some edges to the appointed root-vertices of the base graph.By means of transfer matrix and a finer partition of the embeddings,the explicit formulas for the genus distribution polynomials of four types of ladder-class graphs are derived.展开更多
文摘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.
基金Supported by Scientific Research Project of Hunan Province Education Department(Grant No.17B045)。
文摘Calculating the genus distributions of ladder graphs is a concerned topic in topological graph theory.In this paper,we formulate several ladder-class graphs by using a starting graph iterative amalgamation with copies of a path to construct a base graph and then adding some edges to the appointed root-vertices of the base graph.By means of transfer matrix and a finer partition of the embeddings,the explicit formulas for the genus distribution polynomials of four types of ladder-class graphs are derived.
