About Path and Cycle Graphs

Sebastian Koch

doi:10.2478/forma-2024-0014

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About Path and Cycle Graphs

Formalized Mathematics

Volume 32 (2024): Issue 1 (August 2024)

By: Sebastian Koch

Open Access

|Dec 2024

Abstract

In this article path and cycle graphs are formalized in the Mizar system.

References

Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.
Open DOI Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Ricky W. Butler and Jon A. Sjogren. A PVS graph theory library. Technical report, NASA Langley, 1998.
Search in Google Scholar Back to article
Reinhard Diestel. Graph Theory, volume Graduate Texts in Mathematics; 173. Springer, Berlin, fifth edition, 2017. ISBN 978-3-662-53621-6.
Search in Google Scholar Back to article
Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.
Open DOI Search in Google Scholar Back to article
Sebastian Koch. Introduction to graph enumerations. Formalized Mathematics, 31(1): 31–52, 2023. doi:10.2478/forma-2023-0004.
Open DOI Search in Google Scholar Back to article
Sebastian Koch. About supergraphs. Part I. Formalized Mathematics, 26(2):101–124, 2018. doi:10.2478/forma-2018-0009.
Open DOI Search in Google Scholar Back to article
Sebastian Koch. About supergraphs. Part III. Formalized Mathematics, 27(2):153–179, 2019. doi:10.2478/forma-2019-0016.
Open DOI Search in Google Scholar Back to article
Sebastian Koch. Refined finiteness and degree properties in graphs. Formalized Mathematics, 28(2):137–154, 2020. doi:10.2478/forma-2020-0013.
Open DOI Search in Google Scholar Back to article
Sebastian Koch. About regular graphs. Formalized Mathematics, 31(1):75–86, 2023. doi:10.2478/forma-2023-0008.
Open DOI Search in Google Scholar Back to article
Gilbert Lee. Walks in graphs. Formalized Mathematics, 13(2):253–269, 2005.
Search in Google Scholar Back to article
Gilbert Lee and Piotr Rudnicki. Alternative graph structures. Formalized Mathematics, 13(2):235–252, 2005.
Search in Google Scholar Back to article
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 327–341, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-73086-6. doi:10.1007/978-3-540-73086-6_26.
Open DOI Search in Google Scholar Back to article
Lars Noschinski. A graph library for Isabelle. Mathematics in Computer Science, 9(1): 23–39, 2015. doi:10.1007/s11786-014-0183-z.
Open DOI Search in Google Scholar Back to article
Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd, Edinburgh, 1972. ISBN 0-05-002534-1.
Search in Google Scholar Back to article