Enumeration of 2 -connected Loopless 4 -regular Maps on the Plane

Han Ren, Yanpei Liu, Zhaoxiang Li
2002 European journal of combinatorics (Print)  
In this paper rooted (near-) 4-regular maps on the plane are counted with respect to the root-valency, the number of edges, the number of inner faces, the number of non-root vertex loops, the number of non-root vertex blocks, and the number of multi-edges. As special cases, formulae of several types of rooted 4-regular maps such as 2-connected 4-regular planar maps, rooted 2-connected (connected) 4-regular planar maps without loops are also presented. Several known results on 4-regular maps and
more » ... trees of Tutte are also concluded. Finally, asymptotic formulae for the numbers of those types of maps are given.
doi:10.1006/eujc.2001.0533 fatcat:qp7bfk7o7babhbt3xhtrkokc7m