Asymptotic expansion of regular and connected regular graphs
Combinatorics
2024-09-06 v2
Abstract
We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). We also deduce the asymptotic expansion of connected k-regular graphs using standard techniques for divergent series developed by Wright (1970) and Bender (1975), and quantify its closeness to the asymptotic expansion of k-regular graphs.
Keywords
Cite
@article{arxiv.2408.12459,
title = {Asymptotic expansion of regular and connected regular graphs},
author = {Élie de Panafieu},
journal= {arXiv preprint arXiv:2408.12459},
year = {2024}
}
Comments
13 pages plus 20 pages of proofs and 3 pages of bibliography