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
A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.
In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109...In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, "On the number of eulerian planar maps" that appeared in Acta Math Sinica, 12: 418-423 (1992) is simplified.展开更多
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the National Natural Science Foundation of China (Grant No. 10571013)
文摘A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.
基金the National Natural Science Foundation of China (Grant No. 10271017)
文摘In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, "On the number of eulerian planar maps" that appeared in Acta Math Sinica, 12: 418-423 (1992) is simplified.
