{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T15:33:51Z","timestamp":1777476831671,"version":"3.51.4"},"reference-count":12,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this article regular graphs, both directed and undirected, are formalized in the Mizar system [7], [2], based on the formalization of graphs as described in [10]. The handshaking lemma is also proven.<\/jats:p>","DOI":"10.2478\/forma-2023-0008","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T14:03:23Z","timestamp":1696428203000},"page":"75-86","source":"Crossref","is-referenced-by-count":1,"title":["About Regular Graphs"],"prefix":"10.2478","volume":"31","author":[{"given":"Sebastian","family":"Koch","sequence":"first","affiliation":[{"name":"Mainz , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"key":"2026042801414526865_j_forma-2023-0008_ref_001","doi-asserted-by":"crossref","unstructured":"Broderick Arneson and Piotr Rudnicki. Chordal graphs. Formalized Mathematics, 14(3): 79\u201392, 2006. doi:10.2478\/v10037-006-0010-3.","DOI":"10.2478\/v10037-006-0010-3"},{"key":"2026042801414526865_j_forma-2023-0008_ref_002","doi-asserted-by":"crossref","unstructured":"Grzegorz Bancerek, Czes\u0142aw Byli\u00abski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026042801414526865_j_forma-2023-0008_ref_003","unstructured":"John Adrian Bondy and U. S. R. Murty. Graph Theory. Graduate Texts in Mathematics, 244. Springer, New York, 2008. ISBN 978-1-84628-969-9."},{"key":"2026042801414526865_j_forma-2023-0008_ref_004","unstructured":"Ricky W. Butler and Jon A. Sjogren. A PVS graph theory library. Technical report, NASA Langley, 1998."},{"key":"2026042801414526865_j_forma-2023-0008_ref_005","doi-asserted-by":"crossref","unstructured":"Ching-Tsun Chou. A formal theory of undirected graphs in higher-order logic. In Thomas F. Melham and Juanito Camilleri, editors, Higher Order Logic Theorem Proving and Its Applications, 7th International Workshop, Valletta, Malta, September 19\u201322, 1994, Proceedings, volume 859 of Lecture Notes in Computer Science, pages 144\u2013157. Springer, 1994. doi:10.1007\/3-540-58450-1 40.","DOI":"10.1007\/3-540-58450-1"},{"key":"2026042801414526865_j_forma-2023-0008_ref_006","doi-asserted-by":"crossref","unstructured":"Reinhard Diestel. Graph Theory, volume Graduate Texts in Mathematics; 173. Springer, Berlin, fifth edition, 2017. ISBN 978-3-662-53621-6.","DOI":"10.1007\/978-3-662-53622-3_7"},{"key":"2026042801414526865_j_forma-2023-0008_ref_007","doi-asserted-by":"crossref","unstructured":"Adam Grabowski, Artur Korni\u0142owicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191\u2013198, 2015. doi:10.1007\/s10817-015-9345-1.","DOI":"10.1007\/s10817-015-9345-1"},{"key":"2026042801414526865_j_forma-2023-0008_ref_008","doi-asserted-by":"crossref","unstructured":"Sebastian Koch. Miscellaneous graph preliminaries. Part I. Formalized Mathematics, 29 (1):21\u201338, 2021. doi:10.2478\/forma-2021-0003.","DOI":"10.2478\/forma-2021-0003"},{"key":"2026042801414526865_j_forma-2023-0008_ref_009","doi-asserted-by":"crossref","unstructured":"Sebastian Koch. About graph sums. Formalized Mathematics, 29(4):249\u2013278, 2021. doi:10.2478\/forma-2021-0023.","DOI":"10.2478\/forma-2021-0023"},{"key":"2026042801414526865_j_forma-2023-0008_ref_010","doi-asserted-by":"crossref","unstructured":"Gilbert Lee and Piotr Rudnicki. Alternative aggregates in Mizar. In Manuel Kauers, Manfred Kerber, Robert Miner, and Wolfgang Windsteiger, editors, Towards Mechanized Mathematical Assistants, pages 327\u2013341, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-73086-6. doi:10.1007\/978-3-540-73086-6 26.","DOI":"10.1007\/978-3-540-73086-6"},{"key":"2026042801414526865_j_forma-2023-0008_ref_011","doi-asserted-by":"crossref","unstructured":"Lars Noschinski. A graph library for Isabelle. Mathematics in Computer Science, 9(1): 23\u201339, 2015. doi:10.1007\/s11786-014-0183-z.","DOI":"10.1007\/s11786-014-0183-z"},{"key":"2026042801414526865_j_forma-2023-0008_ref_012","unstructured":"Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd, Edinburgh, 1972. 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