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| ENUMERATION OF ROOTED VERTEX NON-SEPARABLE PLANAR MAPS |
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Citation： |
Liu Yanpei.ENUMERATION OF ROOTED VERTEX NON-SEPARABLE PLANAR MAPS[J].Chinese Annals of Mathematics B,1988,9(4):390~403 |
| Page view： 820
Net amount： 782 |
Authors： |
Liu Yanpei; |
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| Abstract： |
In a rooted planar map, the rooted vertex is said to be non-separable if the verlex on the boundary of the outer face as an induced graph is not a cut-vertex.
In this paper, the anthor derives a functional equation satisfied by the enumerating function of rooted vertex non-separable planar maps dependent on the edge number and the
number of the edges on the outer face boundary, finds a parametric expression of its solution, and obtains an explicit formula for the function.
Partieularly, the number of rooted vertex non-separable maps only replying on the edge number and that of rooted vertex non-separable tree-like maps defined in [4] according to the two indices, the edge number and the number of the edges on the-outer face boundary, or only one index, the edge number, are also determined. |
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