Enumeration of labelled 4-regular planar graphs
Combinatorics
2019-07-26 v3
Abstract
We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be computed effectively as the solution of a system of equations, from which the coefficients can be extracted. As a byproduct, we also enumerate labelled 3-connected 4-regular planar graphs, and simple 4-regular rooted maps.
Keywords
Cite
@article{arxiv.1709.04678,
title = {Enumeration of labelled 4-regular planar graphs},
author = {Marc Noy and Clément Requilé and Juanjo Rué},
journal= {arXiv preprint arXiv:1709.04678},
year = {2019}
}