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

✍ Scribed by Han Ren; Yanpei Liu; Zhaoxiang Li

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 195 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0533

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✦ Synopsis

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 trees of Tutte are also concluded. Finally, asymptotic formulae for the numbers of those types of maps are given.

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