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arXiv · 2406.04753

Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach

Frédéric Chyzak·Marni Mishna
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Abstract

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.

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Frédéric Chyzak, Marni Mishna. 2024-06-07. Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach. https://arxiv.org/abs/2406.04753

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