Accession Number : AD0684523

Title :   ON THE ENUMERATION OF ALMOST BICUBIC ROOTED MAPS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Tutte,W. T.

Report Date : FEB 1969

Pagination or Media Count : 28

Abstract : The task is to enumerate combinatorially distinct rooted bipartite planar maps in which each vertex, with the possible exception of the root-vertex, is trivalent. Two almost bicubic rooted maps are combinatorially equivalent if there is a homeomorphism of the surface onto itself which (1) transforms the vertices, edges, and faces of one map into the vertices, edges, and faces of the other and (2) preserves the root-vertex, its incident edge and/or face. Two such maps are counted as distinct if and only if they are not combinatorially equivalent. Suppose (V1, V2) is a bipartition of the vertex set with the root-vertex in V1. A general formula is established for the number of distinct maps qmn with m = the valency of the root-vertex and n = the number of vertices in V2. (Author)

Descriptors :   (*GRAPHICS, *COMBINATORIAL ANALYSIS), POWER SERIES, THEOREMS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE