ENUMERATION OF ROOTED VERTEX NON-SEPARABLE PLANAR MAPS

In a rooted planar map, the rooted vertex is said to be non-separable if the vertex onthe boundary of the outer face as an induced graph is not a cut-vertex. In this paper, the author derives a functional equation satisfied by the enumeratingfuuction of rooted vertex non-separable planar maps dependent on the edge number and thenumber of the edges on the outer face boundary, finds a parametric expression of itssolution, and obtains an explicit formula for the function. Particularly, the number of rooted vertex non-separable maps only replying on theedge number and that of rooted vertex non-separable tree-like maps defined in 4] accordingto 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.

ENUMERATION OF ROOTED VERTEX NON-SEPARABLE PLANAR MAPS

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.