Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach
<|reference_start|>Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach: By a classic result of Gessel, the exponential generating functions for $k$-regular graphs are D-finite. Using Gr\"obner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regular graphs. The method is sufficiently robust to consider variants such as graphs with multiple edges, loops, and graphs whose degrees are limited to fixed sets of values.<|reference_end|>
@article{chyzak2024differential,
    title={Differential equations satisfied by generating functions of 5-, 6-, and
  7-regular labelled graphs: a reduction-based approach},
    author={Fr'ed'eric Chyzak and Marni Mishna},
    journal={arXiv preprint arXiv:2406.04753},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.04753},
    primaryClass={math.CO cs.SC}
}