A census of boundary cubic rooted planar maps

  • Authors:

  • Wenzhong Liu;Yanpei Liu;Yan Xu

  • Affiliations:

  • Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China;Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China;Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

In this paper, boundary cubic rooted planar maps are investigated and exact enumerative formulae are given. First, an enumerative formula for boundary cubic inner-forest maps with the size (number of edges) as a parameter is derived. For the special case of boundary cubic inner-tree maps, a simple formula with two parameters is presented. Further, according to the duality, a corresponding result for outer-planar maps is obtained. Finally, some results for boundary cubic planar maps and general planar maps are obtained. Furthermore, two known Tutte's formulae are easily deduced in the paper.