{"pk":65048,"title":"Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach","subtitle":null,"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.\n \nMathematics Subject Classifications: 05C30, 12H05\n \nKeywords: Regular graph, enumeration, Weyl algebra, reduction-based integration","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Regular graph"},{"word":"enumeration"},{"word":"Weyl algebra"},{"word":"reduction-based integration"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/91s9p0p0","frozenauthors":[{"first_name":"Frédéric","middle_name":"","last_name":"Chyzak","name_suffix":"","institution":"Inria, France","department":""},{"first_name":"Marni","middle_name":"","last_name":"Mishna","name_suffix":"","institution":"Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada","department":""}],"date_submitted":"2026-04-20T20:03:47Z","date_accepted":"2026-04-20T20:03:47Z","date_published":"2026-04-20T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65048/galley/49858/download/"}]}