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Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach
Published Web Location
https://doi.org/10.5070/C66165705Abstract
By a classic result of Gessel, the exponential generating functions for \(k\)-regular graphs are D-finite. Using Gröbner 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.
Mathematics Subject Classifications: 05C30, 12H05
Keywords: Regular graph, enumeration, Weyl algebra, reduction-based integration