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
In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is ti...In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is tight.展开更多
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.
文摘In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is tight.
