The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which ...The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which is an infinite class of 3-connected simple graphs.展开更多
In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn whi...In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn which is the first class of graphs studied for genus distribution where its genus depends on n.展开更多
Some results about the genus distributions of graphs are known,but little is known about those of digraphs.In this paper,the method of joint trees initiated by Liu is generalized to compute the embedding genus distrib...Some results about the genus distributions of graphs are known,but little is known about those of digraphs.In this paper,the method of joint trees initiated by Liu is generalized to compute the embedding genus distributions of digraphs in orientable surfaces.The genus polynomials for a new kind of 4-regular digraphs called the cross-ladders in orientable surfaces are obtained.These results are close to solving the third problem given by Bonnington et al.展开更多
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
基金The NSF (10201022) of China NSF (1012003) of Beijing City.
文摘The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which is an infinite class of 3-connected simple graphs.
基金supported National Natural Science Foundation of China (Grant Nos. 10571013, 60433050)the State Key Development Program of Basic Research of China (Grant No. 2004CB318004)
文摘In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn which is the first class of graphs studied for genus distribution where its genus depends on n.
基金Beijing Jiaotong University Fund (Grant No.2004SM054)the National Natural Science Foundation of China (Grant No.10571013)
文摘Some results about the genus distributions of graphs are known,but little is known about those of digraphs.In this paper,the method of joint trees initiated by Liu is generalized to compute the embedding genus distributions of digraphs in orientable surfaces.The genus polynomials for a new kind of 4-regular digraphs called the cross-ladders in orientable surfaces are obtained.These results are close to solving the third problem given by Bonnington et al.
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.
