Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach
Abstract
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, 12H05Keywords: Regular graph, enumeration, Weyl algebra, reduction-based integration
Fields of Study & Subjects
Advanced Topics in Algebra
Polynomial and algebraic computation
Numerical methods for differential equations
Publication details
- Journal / source
- Combinatorial Theory
- Publisher
- California Digital Library (CDL)
- Volume
- 6
- Issue
- 1
- Publication date
- 20 April 2026
- Language
- EN